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There are three most challenging objections to the divine (God-authored) inspiration of the Bible; one is science, one is contradictions, and one is it lacks in totality.
The well known Biblical claim of a 6-day (presumably 24-hours per day) appears untenable given fossils, the age of the universe, etc.
Another is the sun and moon standing still.
Then spake Joshua to the LORD in the day when the LORD delivered up the Amorites before the children of Israel, and he said in the sight of Israel, Sun, stand thou still upon Gibeon; and thou, Moon, in the valley of Ajalon. And the sun stood still, and the moon stayed, until the people had avenged themselves upon their enemies. Is not this written in the book of Jasher? So the sun stood still in the midst of heaven, and hasted not to go down about a whole day. Jos 10:12-13
The well-known Easter challenge is based on the so-called contradictory four gospel accounts of the last days and resurrection of Jesus Christ.
Some compare various other verses and find contradictions.
Here is a site for example, although a lack of understanding is fairly apparent. Here is an explaining site.
This third objection is a bit harder to grasp for many Christians because they certainly wouldn't want to affirm that God via the Apostles had left something out of His word as regards salvation. But, by adding Tradition or other Books like LDS Book of Mormon and others, this is what's implied.
The idea that God somehow forgot certain things like the dogma of ever-virgin, but yet that some denominations is necessary to believe for salvation is an impingement on the inspiration.
These objections are well-known and apologists have written extensively about issues within the three categories.
At the same time, as I answered elsewhere, the fact of hundreds of asserted and fulfilled prophecies far outshine the question of 24-hours or 24 zillion hours for God to create.
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"What are the most challenging objections . . . ? "
After over half a century of reading and studying and meditating on the holy scriptures (Genesis to Revelation, 66 books, TR/KJV/YLT/EGNT)(1) I do not find any objection to the inspiration of scripture to have any weight whatsoever. None of the arguments, to me, can be called 'challenging' in the slightest degree.
The scripture, itself, in its entirety, in its veracity, in its integrity and in its power (that is to say the power of the word of God when the Spirit of God utters it to one's own spirit) is of such force that no objection of any kind can stand for a moment in the mind or heart.
There is nothing else on earth which compares, to the slightest degree, to these holy scriptures. Some have attempted to mimic them and at the age of seventeen, purely as an academic exercise, I glanced at these attempts. I found them to have nothing whatsoever in common with that which they attempted to mimic, and I never referred to them again.
(1) TR - The Textus Receptus, the 'Received Text' namely Beza, Stephanus, Elzevir, and Scrivener which agree together save in but few places, none of which are doctrinally significant.
KJV - The Authorised King James Version
YLT - Young's Literal Translation
EGNT - The Englishman's Greek New Testament (Stephens Text) which contains an excellent literal, interlinear translation
These are the 'scriptures' which fill my mind, govern my mentality, and remain firmly in my soul, to the exclusion of all other ideology.
In over half a century, nobody has ever uttered an objection to these scriptures, nor have I ever read one, which had any power whatsoever to dissuade me from them. None of the arguments were to the least degree logical, practical, cogent, or appealing.