What is the argument against the imposition of clerical celibacy as practiced in the Roman Catholic Church?

Institution and codification are not the same thing. Surviving documents dating back to the 5th century "consider the practice to be an ancient and timeless tradition" (source, see footnotes). Wikipedia talks about the codification in the 11th century, but even the early 4th century Council of Elvira passed a law against conjugal relations, with the penalty of being removed from the priesthood.

Protestant churches don't require celibacy because they don't follow Canon Law, and many don't have anything remotely like Canon Law. Some are not large enough to need it, and some are opposed to any sort of "earthly" authority or regulation whatsoever. There's no direct prohibition in Scripture, and for them there's no ecclesiastical prohibition, so they don't uphold the practice. It's really that simple.

If you want the details, here are the practical and theological Protestant points against the Catholic view and practice:

1. The Catholic view of sex is that it is not a "bodily need" that needs to be satisfied, but something that can be entirely avoided by some people, and that celibacy (like fasting) strengthens the will and character. The opposing idea is that nobody should be deprived of something they "need". Some go as far as to say that being deprived of this "need" might even lead to serious psychological disorders (scientifically this is nonsense, but that's the intuition).
2. In Catholicism, the job of a priest is to say the Mass and to administer the Sacraments, and there are a huge number of support groups for personal or family issues. In some other denominations, a pastor must fill the role of a spiritual counsellor, and some believe that if a priest/pastor is married, he'll be able to do an even better job of relating to the problems of his community.
3. Some communities simply wouldn't be able to find someone who is committed to being celibate just to be a pastor. People willing to give up the possibility of marriage are pretty rare.
4. Luther, who had made a vow of celibacy as a priest, abandoned that vow and marred a former nun. Zwingli, also a priest, secretly married shortly before petitioning his bishop to abolish the requirement of celibacy. Calvin was also married, and argued in the Institutes (4.13.20) that vows made concerning things that "God does not at all require of us" are invalid.

The basic idea in that last point is that if I make a vow to smack you over the head, and you don't want me to do that, then I'm "loosed" from my vow. Obviously, whether a priest (like Luther, or Zwingli) were "loosed" totally depends on whether God would say it was a vow worth making and keeping. Catholics think that St Peter and his successors have the ability to "bind" and "loose" people according to tradition, and Calvin, Luther, Zwingli, and Protestants in general don't think anyone has that ability.

How the Vatican imposed celibacy on its priests

The "pious histories" of priestly celibacy tell the story of how Jesus regarded celibacy as part of his prophetic mission. As a result, Catholic priests picked up on this when reading the Gospels, and some embraced voluntary celibacy as a result. Thus, some local Synods passed legislation in favor of priestly celibacy. Only in the twelfth century did a "Vatican Council" legislate celibacy for all future deacons, priests, and bishops throughout the Catholic Church.

In what follows I am not going to try to pass on to you another "pious history." Rather, as a Church Historian, I am going to tell you something of the ugly side of imposed priestly celibacy. In my short history, I will make mention of three reasons for imposing celibacy and three reasons for overturning celibacy. You can check them off as you go.

Pope Paul VI, during the final meeting of Vatican II in 1965, made an extraordinary intervention to forbid any discussion of the rule of priestly celibacy since he had elected to study this issue himself and since he had been warned that some bishops were keen to speak in favor of optional celibacy. Accordingly, on 24 June 1967, Paul VI published his encyclical on priestly celibacy known as Sacerdotalis Caelibatus.

Explaining how he arrived at his decision, Paul VI wrote: “We have, over a considerable period of time earnestly implored the enlightenment and assistance of the Holy Spirit and have examined before God opinions and petitions which have come to Us from all over the world, notably from many pastors of God’s Church” (sec. 1).

To his credit, Paul VI acknowledges having received and prayerfully considered opinions and petitions coming from pastors who presumably favored a change in the rule of celibacy. To his discredit, Paul VI failed to consult the worldwide bishops by letter. He similarly refused to open up this delicate pastoral issue at the tri-annual Synod of Bishops in Rome. Thus, Paul VI effectively bypassed the practice of collegiality affirmed at Vatican II and, in its place, he imposed a treatise of his own choosing and making. (More on this later.)

Every informed pastor (the Pope included) knows that celibacy was not universally imposed upon the clergy until the Middle Ages, but only very few are aware of the history whereby papal attacks on clerical marriage were resisted for many generations by pastors and their wives.

The origins of universal clerical celibacy emerged as an unexpected byproduct when eleventh century church reformers tried to deal with problems surrounding the inheritance of Church properties and of Church offices by the sons of clergymen. Reforming popes initially tackled this problem by trying to reduce the number of “sons” fathered by priests. Priests and their wives were accordingly required to sleep in separate beds. When this approach failed, their wives were required to live in separate houses. Fines were imposed. Priests stubbornly living with their wives were suspended. Bishops were required to make pastoral visitations and forcibly separate priests from their lawfully wedded wives. In many instances, these bishops were often bombarded by angry parishioners throwing rotten fruit. Meanwhile, in other areas, wives of priests who became pregnant were publicly shunned by parishioners and, in some instances, priests wanting to advance their careers within the Church were forced to abandon their wives and children in exchange for a better priestly post.

The First Lateran Council (1123) was so frustrated by the inability of the Vatican to impose compliance to earlier legislation that they took the radical step of declaring the sacramental marriages of priests “null and void.” The Council decreed “that marriages already contracted by such persons [priests, deacons and monks] must be dissolved, and that the persons [both husbands and wives] be condemned to do penance.” In a Church that was endeavoring to sustain the notion that no sacramental marriage could ever be dissolved by anything less than death of one of the spouses, the First Lateran Council’s open hostility toward the sacramental marriages of its priests was a shocking (and many would say “ungodly”) departure from its own theology of the indissolubility of the marriage bond.

There followed three centuries where discovering secret mistresses and illegitimate children became the ongoing concern of the Vatican and reform-minded bishops. Only when the laity were finally persuaded to boycott the altars of priests “living in sin” and bishops began demanding a solemn vow of celibacy prior to ordination did the campaign for clerical “chastity” finally take hold.

All in all, the whole ugly mess surrounding the imposition of celibacy did not approach anywhere near a universal adherence until the seminary system was instituted following the Council of Trent. In the new seminaries, the sexuality of young boys could be closely monitored and their youthful characters could be informed (some would say traumatized) with a morbid fear of having any contact whatsoever with women outside of the confessional.

This opened up the floodgates for developing new theologies calculated to foster clerical “virginity.” Gifted preachers moved from parish to parish promoting this message: “That a priest’s hands ought to be entirely virginal since only then could they worthily bring God into the world [at the words of consecration] just as did the Virgin Mary.” Out of such pietistic theologies that circulated during the 17th and 18th centuries, the charism of celibacy put forward in Paul VI’s Sacerdotalis Caelibatus was developed.

Needless to say, Paul VI, in his encyclical, tells us nothing of the pain, anguish, and understandable resistance to imposed celibacy that marked the eleventh to the sixteenth centuries. Rather, he offers Catholic priests the entirely mistaken and altogether unhistorical impression that priestly celibacy began when Jesus freely chose celibacy as an essential character of his own service to his Father and when he declared that “there are eunuchs [i.e. "castrated males" like myself] who have made themselves [voluntary] eunuchs for the sake of the kingdom of heaven” (Matt 19:12). Paul VI thus leaves the impression that the link between celibacy and priesthood gradually grew within the church and that it gradually came to full flower as an eschatological sign of the life that everyone will one day enjoy for “in the resurrection they neither marry nor are given in marriage” (Matt 22:30). The celibacy of the priest, consequently, was heralded in Sacerdotalis Caelibatus as a foreshadowing of the celibacy that all the Saints would enjoy during “the final stages of salvation.”

Even if the manifest theological and historical flaws within Sacerdotalis Caelibatus could be forgiven in the name of the personal piety of Paul VI, one can hardly overlook the clear evidence of the Gospels to the effect that Jesus never mentioned celibacy when he chooses any of his disciples. Peter, who is clearly recognized as a married man, receives no admonition to separate himself from his wife. But, more importantly, we read in 1 Tim 3:2 that “a bishop must be above reproach, married only once [a one-woman man]” and, in Tit 1:7, we read that a presbyter should also be “someone who is blameless, married only once, whose children are believers.” Instead of discovering a “flowering of Jesus’ gift of celibacy,” therefore, we find in the late apostolic tradition the requirement that bishops and presbyters must have a wife and children. Why so? For this stated reason: “For if someone does not know how to manage his own household, how can he be expected to take care of God’s church [which is an extended family]?” (1 Tim 3:5).

How can Pope Paul VI expect Catholic priests to respect him as a reliable teacher when he fails to notice these things that are clearly named in the sacred Scriptures? And what if he did notice these things but deliberately omitted to mention them because they entirely negate his pious arguments in favor of priestly celibacy? Then, in that case, Catholic priests would have to conclude that Pius VI is a dishonest scholar not worthy of our attention. All in all, this brings us to the embarrassing sticking point of having to decide whether Paul VI is either incompetent or dishonest or a curious mixture of both in his approach to clerical celibacy.

Needless to say, I could not speak so frankly to my seminarians. But oftentimes they would, none the less, confront me with their anxious questions. “What kind of God,” one seminarian urgently asked me, “would call me to be a celibate priest while confounding me with an equally strong call to be a loving husband and father?” For more on this, go to https://www.churchonfire.net/2014/10/14/when-a-priest-falls-in-love/

With the renewal of the Church following Vatican II, hundreds of thousands of priests anticipated a relaxation of the rule of celibacy. The adamant position taken by Paul VI in his encyclical Sacerdotalis Caelibatus killed their hope for any compassionate change. Many Spirit-filled priests, facing a crisis of conscience between their call to ministry and their call to marriage, decided to apply for laicization. All told, 200,000 priests worldwide left their ministry in order to marry. Those who stayed called for more compassion, more collegiality, and more discussion on this matter. In 1970, the distress and disappointment of priests regarding Sacerdotalis Caelibatus had become so publicly known that nine German theologians, including Joseph Ratzinger (later Pope Benedict XVI), signed a letter publicly calling for a fresh discussion of the rule of celibacy. It never happened.

The spinoff of all this distortion of history, misreading of the bible, and addiction to authoritarianism is that the Roman Catholic Church is the only major denomination that has an "acute shortage of ministers." At one ordination in the cathedral church, my Archbishop launched into a homily on the "alarming priest shortage." He summed up the cause of this shortage as due to "selfishness" on the part of young men. "They are unwilling even to try celibacy as a spiritual discipline in their choice of vocations." It was hard to listen to this disparaging analysis.

But now I see a ray of hope in Pope Francis. Right from the very beginning, he began saying publicly, "Clerical celibacy is not a dogma." So, even within the office of the papacy, a new era of refreshing honesty is emerging. It is only a matter of time before "optional celibacy" will be authorized and practiced. Then the fake histories, the fake theologies, and the fake use of the NT will finally be exposed.

Protestants take the priestly celibacy as unbiblical or unnatural.
They claim that every man must obey the biblical injunction to "be fruitful and multiply"(Gen. 1:28) and Paul command that "each man should have his own wife and each woman her own husband"(1Cor. 7:2). They also argue that celibacy somehow causes illicit sexual behaviour or perversion or at least correlates with higher incidence of it.

Although most people are at some point of their lives called to the married state, the vocation of celibacy is explicitly advocated as well as practiced by both Jesus and Paul. Paul actually endorses celibacy for those capable of it. (1Cor. 7:8-9).He specifically clarifies:

1 Cor. 7:6-7 I say this as a concession, not as a command. I wish that everyone was as I am. But each has his own gift from God, one this way, another that.

Paul prefers celibacy in 1 Cor.7:27-34) and

1 Cor. 7:38 So then, the one who marries his own virgin does well, but the one who does not, does better.

After Jesus teaching in Mat. 19 on divorce and remarriage, the disciples exclaimed, "If such is the case of a man with his wife, it is not expedient to marry (Matt. 19:10). This remarks prompted Jesus' teaching on the values of celibacy "for the sake of the kingdom"(Matt. 19:11-12).

Protestant reject celibacy considering it as a dogma or a doctrine of Catholic Church and maintain that priestly celibacy was made mandatory much later in the Church history:

It is taken by protestant as a central and irreformable part of Catholic faith, believed by Catholic to be coming from Jesus and the apostles and their objection is that, since Peter was married (Mark 1:30) there cannot be basis for this in Bible.

In reality the celibacy is not the rule for all Catholic priest even today. In Eastern rite Catholics, married priest are the norm, just as they are for Orthodox and Oriental Christians. In Eastern churches married men may become priests, unmarried priest may not marry, and married priests, if widowed, may not remarry. In western or Latin-rite Church the tradition has been for priests as well as bishops to take vows of celibacy, a rule that has been firmly in place since the early Middle Ages, with exception to those who are married priests in Latin-rite, who are converts from Lutheranism and Episcopalians. So all these variation in Catholic church indicates that priestly celibacy is not an unchangeable dogma but a disciplinary rule. Just as the Peter was married so also any of the nearest pastor of Maronite Catholic Church and both are not contrary to what Catholic faith teaches.

Protestants argue that only a man who has demonstrably looked after a family is fit to care for God's Church and an unmarried man is somehow untried or unproven. This is what Paul taught in 1 Tim. 3:2, 4-5.

This is a literal interpretation of the scripture which leads to further absurdities. With the next verse it implies that only those who have children can become bishops. Further to this it implies that only those who can keep their children submissive and respectful in every way can become bishops and so on.

This literal interpretation creates another contradiction. Paul himself was eminent Church leader, was single and happy to be so. Unless Paul was hypocrite he could have hardly imposed a requirement on bishops that he did not himself meet. The point of Paul's requirement that a bishop be "the husband of one wife" is not that he must have one wife, but that he must have ONLY one wife. Conversely, Paul is saying that a bishop must not have unruly or undisciplined children(not that he must have children who are well behaved), and must not be married more than once(not that he must be married).

Lastly Protestants argue that by requiring at least some of its clerics not to marry, the Catholic Church falls under Pauls condemnation in 1 Tim.4:3 against apostate who "forbid marriage".

1 Tim.4:3 They will prohibit marriage and require abstinence from foods that God created to be received with thanksgiving by those who believe and know the truth.

In fact Catholic church forbids no one to marry. No one requires to take a vow of celibacy and those who do so take it voluntarily. They renounce marriage (Matt.19:12); no one forbids it to them. Any Catholic who doesn't wish to take such a vow doesn't have to, and he is always free to marry with Church's blessing. The Church simply elects candidates for the priest hood from among those who voluntarily renounce marriage.

Paul was actually referring to Gnostic sects through the ages that denounced marriage, sex and body as intrinsically evil. Some early heretics fit this description as did the medieval Albigensians and Catharists.

Celibacy is an eschatological sign to the Church, a living-out in the present of the universal celibacy of heaven: "For in the resurrection they neither marry nor are given in marriage, but are like angles in heaven"(Matt. 22:30)

Clerical Celibacy was not instituted in the eleven hundreds, it was established 800 years before by Emperor Constantine I at the Council of Nicaea in 325.

Canon 3

The great Synod has stringently forbidden any bishop, presbyter, deacon, or any one of the clergy whatever, to have a subintroducta dwelling with him, except only a mother, or sister, or aunt, or such persons only as are beyond all suspicion.

I would like to add a few other Biblical reasons Protestants in general will allow for married Pastors.

Simon's mother-in-law was in bed with a fever, and they immediately told Jesus about her. -Mark 1:30.

Simon Peter having a mother-in-law necessarily meant that he had a wife. If one of Jesus's own apostles had a wife, then right there is pretty good evidence that pastors today can likewise have wives.

Here's an argument Paul makes about the matter in 1 Corinthians 9,

3 This is my defense to those who sit in judgment on me. 4 Don’t we have the right to food and drink? 5 Don’t we have the right to take a believing wife along with us, as do the other apostles and the Lord’s brothers and Cephas[a]? 6 Or is it only I and Barnabas who lack the right to not work for a living?

As we already know that one of the other apostles had a wife, we can safely say that Paul isn't being sarcastic here, but rather stating a very straightforward argument. The apostles were allowed, among other things, money and the right to marry; however, the apostles would at times choose to give up their rights for various reasons, as Paul and Barnabas did with wives, and others did at various points with money among other things (see 1 Cor. 9:12).

Just because some honorably chose to give up those rights, doesn't in any way mean they didn't have those rights in the first place, as Paul states here.

As Protestants don't follow the headship of the Catholic church, they likewise don't observe the things that the Catholic church claims to have "loosed" or "bound," and the scriptural evidence taken without that external input supports a pastor who has the full right to marry if he so chooses.