How can Protestants authoritatively declare something wrong or heretical under Sola Scriptura?

So upon what basis can Protestants insist that some teaching contradicts the Bible objectively, and not only according to their own personal understanding of the Bible (which most would admit could be wrong)?

I cannot speak for other Protestants, but when I claim that a teaching contradicts the Bible objectively, I do so on the basis that the falsehood of the teaching is a necessary inference from what is written in the Bible.

To answer this by claiming that my inference is really only my personal understanding of the Bible, and that I could be wrong, is not an argument, but is instead a refusal to even offer an argument. It's the same error that the sluggard makes in Proverbs 26:13, in that it treats the possibility of something as an actuality.

If you want me to believe that my claim about what the Bible teaches is only my own personal understanding, and is objectively wrong, you need to offer more than assertions.

Disclaimer

I’m trying to grasp your question and for fear of being told off in the comment section I’ll turn my comments for clarification into an answer. If I misunderstood your question in light of my answer I apologize in advance.

Analyzing Calvinism

Firstly I found it peculiar that you included Calvinism alongside denominations.

I’ll try to illustrate my response with Calvinism why I would call Calvinism heretical and not merely a matter of conflicting opinions among Christians.

[I’m no Calvinist, certainly not an Arminian (a sub-branch of Calvinism, Arminius was a devout Calvinist as he wrote so much himself and thus a false dichotomy), nor a Traditionalist. I hold a view that currently doesn’t actually have a title but is common. Maybe you could call me a non Calvinist with respect to this subject.]

The measure I would use for Calvinism is, does it align with Scripture or not. And it doesn’t, in fact it contradicts Scripture.

Regeneration precedes Faith

For instance Calvinism’s “regeneration proceeding faith”. It is unScriptural and illogical. It places the emphasis on being The elect as a qualifier and not one’s faith in the finished work of Jesus Christ. It claims that first a person is regenerated/born again and then they can believe. This is necessary because of other doctrines Calvinism holds to be true and they build on each other, Scriptural intergrity is sacrificed in favor of the presupposition.

But Scripture says in many verses that faith proceeds regeneration while there are no verses, none, that support Calvinistic doctrine which demands regeneration to precede faith.

“yet you refuse to come to me that you may have life.” ‭‭John‬ ‭5:40‬ ‭

Notice first you come to Jesus (an act of faith or through faith) then you have life (regeneration/born again). There are many many verses.

Method

So essentially the method would be start with passages of Scripture that have clear simple understanding or classic passages of Scripture. Then approach and interpret passages in the Bible that are more obscure (difficult to understand) in the light of the clear passages. And afterwards any presuppositional understandings that originate outside of Scripture like Calvinism, which is philosophical and draws it’s roots from Augustinian Manichaean Gnosticism will be exposed as heretical and non Scriptural.

One should never approach Scripture attempting to validate their presuppositions.

But if you start with a presupposition, you allow a philosophical presupposition to color the obscure interpretations of a text, those passages that are not understood very easily and this in turn reinterprets the clear and classic passages of Scripture in light of the presupposition.

The context is not the clear passages of Scripture but the philosophical construct. Without realizing it, you have redefined words/Scripture to fit a doctrine rather than developed a doctrine to fit Scripture.

“and he died for all, that those who live might no longer live for themselves but for him who for their sake died and was raised.” ‭‭2 Corinthians‬ ‭5:15‬ ‭ESV‬‬

The word all no longer means all but is changed to mean the elect. Likewise John 3:16, Jesus didn’t die for the world (all) but for the elect and thus simple understanding of clear passages are reinterpreted through the new definition of obscure passages facilitated by the presupposition coloring of the obscure passages. Presupposition therefore trumps clear Classic Scriptures. Or extraBiblical philosophy trumps Sola Scriptura and that is heresy making for bad hermeneutics and exegesis.

So that’s how I would critique is a doctrine, philosophy and/or presupposition is heretical or Biblical. Start with clear Scripture -> interpret obscure Scripture -> clarify or eliminate presuppositions

Heresy occurs when this approach is reversed.

(I don’t want to turn this answer into a refutation of Calvinism so I’ve limited my answer to one/two examples.)

To make 'a statement based on opinion', Sola Gratia is, imho, a better thing than sola scriptura.
Take the Nicean Creed, for instance. Both sides of the debate strongly believed in the scriptures.
Or take John 6: 52-56, which is not truly believed by many protestants and yet is a much treasured belief of Catholics.
And Jesus impressed the crowds, not because He knew the scriptures so well (which He did, of course) but because He spoke with authority. He would say that Moses said such and such 'but I say to you...'.
The scriptures are inspired by the Holy Spirit. And it is by the Holy Spirit that the words are made real/ revealed in our lives. Not by scripture alone. This is how Peter came to believe that Jesus is the Messiah.
And that encouraged another 'I say to you...'(Matthew 16:18)

Introduction

While I would argue that most protestants aren't actually Sola Scriptura, I think that discussion is probably beyond the scope of the question here. The problem with your question is that it supposes that Sola Scriptura and official church doctrine, a catechism, and so forth are mutually-exclusive and that any given protestant operates under their own authority.

Protestant's have canon law

This, however is not the case. The United Methodist Church, for example, has formal church teachings roughly equivalent to the decretals, creeds, statements and other official teachings of the Catholic Church. (some of these teachings include creeds and statements of the Catholic Church prior to the reformation; a fact true for most Protestant denominations) Just as Ecumenical Councils will release statements, the UMC will often ratify and publish official church doctrines at Annual Conferences or General conference. The UMC also has Confirmation, complete with classes roughly equivalent to Catechism.

Anglicans also have assemblies at which doctrine is formulated, Catechism, and official church doctrine, as does the Episcopalian denomination, the Lutheran Church, the Presbyterian Church. As such, these and many other Protestant denominations do have canon law (not to be confused with Biblical canon) to which an individual layperson or clergy member can appeal to as an authority. The main difference here is that the denominations noted do not claim divine inspiration for canon law and the teaching's of church leaders.

Not all protestants believe Sola Scriptura

While this may be true for the aforementioned denominations, it is not true for Jehova's witness, Latter Day Saints, and some other Protestants. For example, LDS teaching believes that the teaching's of the Prophet are divinely inspired, roughly equivalent to the pope, (and Latter Day Saints do have formal church teachings such as Doctrine & Covenants, teachings of the prophets, and books and manuals like Gospel Principles, True to the Faith, and others.) Latter Day Saints also have seminary, which is roughly equivelant to Catechism, and due to their belief in the divine inspiration of the Prophet's teaching's reject Sola Scriptura teachings.

Furthermore, The Methodist Church has a principle of Prima Scriptura - which they distinguish from Sola Scriptura in that they believe that things besides The Bible (Tradition, reason, and personal revelation) have a hand in defining truth, but that scripture is the main or final authority.

This problem exists in Catholicism

Catholicism is also susceptible to this concern as well and has suffered several schisms. The Eastern Orthodox and Roman Catholic churches have, at times, conflicting teachings (not to mention leaders). There are also the [Oriental Orthodox], not to mention the Assyrian Church and Western Schism - all of these could be considered "denominations" in Protestant parlance. This points to the fact that even outside of Protestantism there is no universal definition of theology or how to understand the Bible with all of these groups conflicting (or having conflicted at one point or another) to some degree.

Conclusion

As such, in general protestants have some or most of the same basis and similar authorities to which they can appeal to insist that a given teaching contradicts the Bible as objectively as any Roman Catholic can,

This can be done to a degree similar to which any Roman Catholic can do so without the basis of their own personal understanding of the Bible, and most protestants have as much validity to claim that their church's leadership got it "right" as the Vatican does.

And this is notwithstanding the question of whether any Roman Catholic can truly claim that their interpretation is not truly their own personal one be it filtered through their church's teaching or by direct engagement with the books of The Bible (Protestants have similar issues with the claim of Sola Scriptura - can you truly claim Sola Scriptura if your interpretation is your own personal one since any individual protestant is not infallible and they are not The Word Himself - again outside the scope of this question).

This also comes with the disclaimer that this is a generalization of protestantism - there are obvious exceptions to this such as the Uniterian Universalist church that would respond by saying "Indeed! How can anyone claim that their truth is not subjective?" and would conclude "Therefore, aren't we all be right?"

Warning: I am still working on the final version of this answer, so this is a draft. As we all know, this is a highly complex issue that is interconnected with canon formation, creeds, rule of faith, various church fathers position, how the 1st generation apostles view scriptures, oral tradition, elements of the Protestant doctrine of Scripture (inerrancy, authority, sufficiency, etc.), Reformer's understanding, terminology ambiguity (esp. "tradition"), and most importantly (for the OP question) epistemological issues by today's Protestants in actual application of the "sola scriptura" principle.

From time to time I'm editing it to include resources that I find helpful, but until this warning is removed, please consider this as a draft and post comments in this chat room. My goal (maybe a year away) is to have an answer that will be satisfactory to the OP and commenters, Protestants and Catholics alike.

Most lay Protestants today think Sola Scriptura to mean Bible only, no tradition at all. But the original reformers (including Luther & Calvin) have always included a measure of apostolic tradition in their Sola Scriptura principle. The original reformers carefully stayed away from the highly individualistic, divorced from any tradition approach that Sola Scriptura came to mean today. I highly recommend reading two scholarly papers on the subject, tracing the historical development of Sola Scriptura and how major figures in the Reformation and the Counter-reformation understood it:

• Sola Scriptura: What did it mean? And what became of it?, a 2017(?) paper by an Irish Catholic Bible scholar & Augustinian friar Kieran J. O'Mahony, OSA
• Solo Scriptura - The Difference a Vowel Makes a 2007 article by Dr. Keith Mathison, a Reformed Professor of Systematic Theology, published in the Modern Reformation magazine 16/2 issue. He also wrote the 2001 well-cited book The Shape of Sola Scriptura whose table of contents can be found here. He defended the thesis of the book in a 2011 reply to a 2009 blog article questioning the book's thesis.

Both scholars, from the opposite ends of the debate about Scripture vs. Tradition, actually shows a convergence of understanding of how Bible interpretation cannot be divorced from tradition. In contrast with most lay Protestants, most Protestant scholars I have encountered, Evangelicals included, by now have realized that a certain amount of tradition is logically necessary to constrain Bible interpretation within a certain boundary which is often named orthodoxy (not to be confused with Eastern Orthodox church), apostolic tradition (not to be confused with how the Catholic church understands Tradition), or the rule of faith / analogy of faith.

Most scholars teaching in seminaries for recognized Protestant denominations such as Southern Baptist, Presbyterian, Anglican, Methodist, even Pentecostals (BUT excluding Jehovah Witness, Latter Day Saint, and possibly 7th day Adventists; some more research needed) would agree that they accept apostolic tradition guiding their bible interpretation up to at least the Council of Nicaea (AD 325), and therefore would affirm both the Apostle's Creed and the Nicene Creed. They could even agree on the creed issued by the Council of Chalcedon (AD 451), for example see one denomination's stand on it.

Before answering your question it's very helpful to FIRST classify the concept of Sola Scriptura into 4 classes following Dr. Keith Mathison's analysis in his book "The Shape of Sola Scriptura", quoted by the Wikipedia article of the book. Most Protestant scholars would advocate Tradition I (especially those following the magisterial reformation model), while Tradition 0 represents fundamentalists, uninformed lay Protestants, and heretics on the Protestant side (such as open theism). Tradition II is where the Catholic church stands, with the danger of going more extreme towards Tradition III, which Friar Kieran O'Mahony implicitly warned at the conclusion of his paper referenced above.

After clarifying the kind of tradition that most enlightened Protestants will wholeheartedly embrace (Tradition I) it is a lot easier to answer your question, since we now have an objective basis to define what is "biblical" and what is not. For example, Jehovah Witness and Latter Day Saints can now be labelled as heretics without needing to appeal to Holy Spirit or subjective personal understanding (because both movements don't accept the Apostle's creed and the doctrine of the Trinity). Rather than repeating other examples and details, I refer you to both papers above (one Catholic, one Protestant) because both scholars have provided objective basis to apply Sola Scriptura principle to Bible interpretation.

ADDENDUM (DEC 2019):

Surveying the blogosphere, "journalsphere", and "booksphere", I selected 3 recent well-written articles and 1 book by "credentialed" authors (i.e. holding a PhD from a seminary, or a professor) writing about the Rule of Faith as a guide to interpret the Bible in an objective manner without subscribing to a notion of Tradition the way the Roman Catholic church understands it (Tradition II). While the authors may not explicitly associate their positions with Mathison's Tradition I, I think it's roughly the same. All of them, in their own way, should provide Protestants the objectivity to pass judgment on heretical beliefs.

1. Martin Luther, the Rule of Faith, and the Bible by Todd Hains, a Dec 2019 article in Mere Orthodoxy, a journal of Christian Humanism taking the cue from C.S. Lewis & G.K. Chesterton.
2. The Rule of Faith and Biblical Interpretation in Evangelical Theological Interpretation of Scripture by Adriani Milli Rodrigues published in Themelios 43.2 (2018) issue.
3. Beyond "Two Source Theory" and "Sola Scriptura": Ecumenical Perspectives on Scripture and Tradition by Candida R. Moss published in Acta Theologica 2015 35(2) issue
4. Reformed Catholicity - The Promise of Retrieval for Theology and Biblical Interpretation, a Jan 2015 Baker Academic book by Michael Allen and Scott R. Swain reviewed in First Things magazine, Jan 2015 issue: The Word and the Rule of Faith by Peter J. Leithart.

OP: How can Protestants authoritatively declare something wrong or heretical under Sola Scriptura?

First of all, one must be very clear about the definition of Sola Scripture (SS). It is the belief that scripture is the sole rule of faith and practice. One must understand that. If one doesn't, then answers (or downvotes about this answer) will reflect that short coming.

To apply this belief, let's take something easy. Let's say you go to church and the priest says "to be saved, you must eat fish on Fridays and if you don't, you'll go to hell forever". This, the priest intones, is de fide (of the faith, without which you go to hell).

Now, how do people know if this belief is true or not? Under SS, it is easy to determine. Where in scripture is this teaching? Ahh, it can't be found. Therefore, I declare it is wrong and heretical under SS.

If this example sounds a bit trite, then one may review history and find plenty of egregious doctrinal errors that those of scripture PLUS XYZ follow that one may also compare against the belief of sola scriptura as the rule of faith and practice.

Apparently more examples are warranted.

SS is the sole rule of faith and practice.

Shall we play guitar or not? Shall we have a pope or not? Shall we have 7 spouses or not? None of those examples on the surface has anything to do with your salvation. But, if someone says, you have to play electric guitar or an organ in your church to be saved, what does SS say? If someone says you have to submit to the Pope of Rome to be saved, what does SS answer? If someone says you have to have a tri-fold hiercharcy in your leadership to be saved, what does SS say? If someone says you can't work on the Sabbath, what does SS say? If someone says you have to believe on the Lord Jesus Christ, what does SS say?

If someone says your baby must be water baptized to be saved, what does SS say? If someone says you must believe that Mary was born immaculate to be saved, what does SS say? If someone says, you must believe Jesus Christ was born of a virgin to be saved, what does SS say?

So again, how can a Protestant authoritatively declare some presumed salvific issue wrong or heretical under SS? It is because a Protestant would say SS is the sole rule of faith and practice.

PS To add, the OP question shows some confusion. SS isn't specifically about interpreting a passage of Scripture, rather it is about agreeing that Scripture will be the sole rule of faith and practice.

The idea of a supreme "interpreter" of Scripture is a separate question. For example, the Catholic Church could remain its own interpreter, but change its official source of information to Scripture Alone (not Scripture and Tradition). Understand the distinction?

When you start by claiming, “Within Protestantism there is no universal definition of theology or how to understand the Bible…” that risks distortion of the facts. Good though the question is, it needs to be pointed out at the outset that the definition of theology is not a problem, let alone a question, among Protestants. All Protestants are agreed that theology is the study of God (‘Pilgrim Theology’ Michael Horton, p 13 para 1). All Catholics and even non-theists are agreed that theology is the study of God. I respectfully suggest that the word ‘doctrines’ ought to replace ‘theology’ in your opening statement. That might sound pedantic but there is a crucial difference between theology and doctrine, which I hope you will not take offence at my mentioning.

The linked claim, that Protestants have no universal definition of ‘how to understand the Bible’ requires clarification. All Protestants agree that a massive breakthrough in understanding the Bible came with translation of it from Latin into vernacular languages, such translation being based on the original languages of the Scriptures, and not on Latin translations. That was rapidly followed by Martin Luther coming to grips with how the Scriptures exposed doctrinal errors and bad Catholic practices in his era, and deciding to stand on the authority of scriptural teaching alone. That remains the basis for all Protestant unity on how to understand the Bible – on the basis of its supreme authority due to its divine inspiration.

Now, it’s obvious that Protestant denominations have, over the years, diverged in their understanding of some doctrines contained in the Bible, and in orders of service, forms of baptism etc, and I take your point there. I would just say that none of that prevents Protestants authoritatively declaring some beliefs and/or practices to be heretical, due to their Sola Scriptura stance. I would add that that does not entail ‘personal interpretations’ or one of Jesus’ sheep hearing the Good Shepherd’s voice say something another sheep does not hear. What you raise there is the problem common to all Christians in all and every denomination you care to mention: ulterior motives or incomplete grasp of Scripture causing them to attach more importance to some points than other Christians do. The Bible itself warns Christians not to argue about words, or ‘disputable matters’ that cause divisions, but sinful human nature being what it is, that sadly happens. Protestants are more prone to that than Catholics, but surely only because they attach more worth to the Bible, and more time to studying it, than do Catholics, who largely seem happy to just accept doctrine and practice as set forth in a system of sacerdotalism that is anathema to Protestants. It would appear that Catholic bishops make declarations about heresy based on a papal and priestly power and authority structure (sacerdotalism) which the laity just accept, giving an appearance of more unity than with Protestants, when in reality it’s due to unquestioning acceptance of papal authority, not individual desires to plumb the depths of the truth and authority of the Bible. (I gladly allow for individuals like yourself being the exception to that general point.)

All Protestants are agreed on crucial aspects of doctrine, such as those set forth in the Apostles’ Creed, and with that we are united with Catholics and Orthodox. Those fundamentals of the faith are in no doubt and we, like you, and like the Orthodox, do declare pseudo-Christian groups to be heretical due to their deviations from those essential doctrines. Our basis for declaring such deviations to be heretical are exactly the same as yours – the Bible states clear doctrinal matters which must never be deviated from. As stated in the NT letter of Jude, verse 3, Christians are to "contend earnestly for the faith which was once delivered unto the saints". All necessary doctrinal faith was conveyed through the apostles and in the Scriptures by the time the last book of the Bible had been written, which was before the end of the 1st century. Thereafter, there can be no 'new doctrine'. That is the error of pseudo-Christian groups (which part of Grateful Disciple’s answer proves). And that, precisely, is one reason why Luther took a stand against ‘new’ doctrines and bad practices that had crept into the Catholic church of his era. He went back to scripture and compared what he saw there with what he saw going on around him, and the difference was startling. Of course, there was no disagreement regarding essential doctrines such as the bodily resurrection of Christ, the Triune Being of God etc. It was stuff that had crept in over the centuries, new doctrines, that a return to Sola Scriptura exposed as heretical.

I suggest that what you are dealing with in your question are secondary matters that do not enter into the realms of heresy. Protestants do disagree on many secondary issues of the faith, but they would not call those things heretical because they are not essential to salvation. When it comes to declaring any doctrine ‘heretical’, Protestants confine themselves to the fundamentals of biblical doctrine and faith, and they stick to a Sola Scriptura basis for that.

To conclude, I would quote from Martin Luther as confirmation of Nigel’s point, in his answer, that “in genuine Protestantism, the Head of every man is Christ. There is no hierarchy.” These quotes shows why Protestants look to Christ, and not a collective hierarchy of men, to know what Scripture teaches as to sound doctrine or heresy. Here Luther deals with channels of God’s self-disclosure ordained for man – the Word and the Sacraments. Yet the Word is not to be equated with Scripture nor with the Sacraments, though it operates through them and not apart from them. The ‘Word’ is not the Bible as a written book because:

“The gospel is really not that which is contained in books and composed in letters, but rather an oral preaching and a living word, a voice which resounds throughout the whole world and is publicly proclaimed.”

This Word must be heard. This Word must be pondered: “Not through thought, wisdom, and will does the faith of Christ arise in us, but through an incomprehensible and hidden operation of the Spirit, which is given by faith in Christ only at the hearing of the Word and without any other work of ours.”

More, too, than mere reading is required: “No one is taught through much reading and thinking. There is a much higher school where one learns God’s Word. One must go into the wilderness. Then Christ comes and one becomes able to judge the world.”

Likewise, faith is given to those who avail themselves of those outward rites which, again, God has ordained as organs of revelation, the Sacraments. Speaking of God and how he can be ‘found’ in the material creation, Luther made clear that: “…yet he does not wish me to seek him apart from the Word… He is everywhere, but he does not desire that you should seek everywhere but only where the Word is. There if you seek him you will truly find, namely in the Word. These people do not know and see who say that it doesn’t make sense that Christ should be in bread and wine. Of course Christ is with me in prison and the martyr’s death, else where should I be. He is truly present there with the Word, yet not in the same sense as in the sacrament, because he has attached his body and blood to the Word and in bread and wine is bodily to be received.”

Luther maintained that true Christianity is apprehended by faith channelled through Scripture, preaching, and Sacrament. That is why he avidly promoted the study of Scripture in church and school. In church, the pulpit and the altar must each sustain the other. Right doctrine is only obtained through Scripture alone as disclosed via the Word of God. And Christ is the sole revealer. A Christless approach to Scripture will result in corruptions. Source: ‘Here I Stand’ Roland Bainton, pp224-5 (Lion 1988 reprint, Britain)

How can Protestants authoritatively declare something as wrong or heretical under Sola Scriptura?

Actually, we have a perfect example in Jesus. Jesus, when he lived on earth as a man, constantly quoted the scriptures of the Old Testament as a way to rebuke the errors of His days. Even as a child, who "grew, and waxed strong in spirit" Luke 2:40, the rabbis and priests at the Jewish temple were astonished at His understanding and answers. And as He "increased in wisdom and stature" Luke 2:52, the people "marvelled, saying 'how knoweth this man letters having never learned?'" John 7:15.

With "it is written", Jesus rebuked with authority the hypocrisy of the Pharisees, and the traditions established by the rabbis and priests as heretical (even though the Jewish priesthood was actually a system established by God at the time!). The fact that He defeated Satan with "it is written" at the temptation, sheds light on the plain authority of the scriptures.

"To the law and the testimony: if they speak not according to this word, it is because there is no light in them (Isaiah 8:20).

The situation is still the same today. The same Spirit that gave inspiration to erring men to write scripture that is inerrant, give also the wisdom to other erring man to interpret scripture with authority. I would wager that it was the Spirit of God that led the reformation and us out of scriptural darkness, and if we had met Luther, or Wycliffe, or Huss, or Zwingli or even Calvin, today we would be able to discern the Spirit of God in them and the authority with which they spoke. They cared not for their own lives for the sake of truth, and many were persecuted by the established authorities and laid their lives down at the stake. Of course, light is progressive, after centuries of spiritual darkness (where the Bible was essentially closed to the laity), it is not possible for one person to have rediscovered all the light in one lifetime. This is why we have progressive truths presented by holy men like Wesley and many more, all of which present the Bible as the basis of their faith. The reformation had presented to the world an open Bible, unsealing the precepts of the law, and reigniting Isiah 8:20.

The fact that we have differing denominations today who all claim sola scriptura is simply the result of freedom of conscience. And just because we differ now, does not mean the Spirit of God will not call together all who truly seek the truth in the future. "Come out of her, my people, that ye be not partakers of her sins" Rev 18:4. It also does not mean that, we can't have the proper authority to rebuke error through the scripture. We look to Jesus as the example, "he that is is spiritual judgeth all things" (1 Cor 2:13). Nor do we need to lay out pages of procedure on how to judge something is against scripture, it did not exist in Jesus' time either.

Finally, the Bible is clear in Revelation that, despite the differences, God will always have a remnant on earth who live according to the truth revealed. These people keep keep the commandments of God (which is found in scripture) and have the testimony of Jesus.

"the remnant of her seed, which keep the commandments of God, and have the testimony of Jesus" (Revelation 12:17).

Speaking as a lifelong Protestant, I would say that in genuine Protestantism, the Head of every man is Christ. There is no hierarchy. None is above another. The greatest is as the least. But it is true that a man's gift will make room for him and spiritual men will appreciate and be voluntarily subject to others more spiritual than themselves.

I have added this edit in answer to the comment made below. It is fundamental to what Protestantism is. Otherwise the question itself becomes invalid as it is not a question that can be asked of Protestantism. (Though it could be asked of other, hierarchical bodies or of hierarchical and individualistic particles of Protestantism).

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The short answer is that if one is utterly meticulous in one's study of the scriptures - in their original language - then there will be no ambiguity, no latitude for personal interpretation, no question of opposing arguments and there will be one, single expression of truth.

It can be seen - and it can be proved by many examples - that the reason for conflicting movements in Protestantism is the untutored, undisciplined, inexact and ignorant expressing of what is advertised as 'biblical' but is in fact not meticulous enough in its expression of the word of God.

These holy scriptures leave me stunned at their accuracy, their careful wording, their staggering revelation and their consistency throughout many volumes by multiple authors over a period of, I would say, just over two thousand years.

It is staggering.

My own, personal, Protestant studies, after twenty five years of tutorage and twenty five more of personal searching, leave me in no doubt that :

Knowing this first, that no prophecy of the scripture is of any private interpretation. For the prophecy came not in old time by the will of man: but holy men of God spake as they were moved by the Holy Ghost. [II Peter 1:21 KJV]

The problem is that unholy men, who are not filled with the Holy Spirit (or even holy men who are, temporarily, swayed by nature and not spirit) speak forth things that they should not.

However even then, their peers ought to be able to correct them, as Paul corrected even the Principal Apostle Peter, to his very face, when he was to be blamed, Galatians 2:11, in a matter of Christian doctrine and resultant Christian practice, and this at a time of crisis when even Barnabas was almost carried away as well, in the dissimulation.

Had this been a Catholic situation Pope Peter would have prevailed and we would all have to be circumcised.

But Paul Protested - and quite rightly so.

For the Lord himself is above all and he says :

I will build my church [Matthew 16:18 KJV]

and he does so . . . in every generation.