There are things which, when you are an inerrantist, never cross your mind, and yet when you cease to be one, you wonder how you could possibly have failed to think those thoughts, notice those things, and ask those questions.
A case in point: the New Testament authors did not write as though they believed their writings to be inerrant.
The case of the Gospel authors who rework and transform the Gospels which went before them is a fairly obvious example. But Paul’s letters likewise confirm this point. He doesn’t simply make statements of fact, or issue commands. He seeks to persuade. He corrects himself at times. He writes like we would expect a human being writing letters to write, not as we would expect God causing his words to flow through a human vessel to write.
And indeed, that last view (as Pete Enns, citing Lesslie Newbiggen, recently pointed out) more akin to the Islamic view of Muhammad and the Qur’an, than to a viable Christian view of Scripture.
But perhaps the most interesting aspect of this is that, since these authors never affirm their own inerrancy, it took the later church to come up with the view that those writings are inerrant. And since Biblical inerrancy is typically a Protestant view, you have to ask: was the church that defined the contents of the canon, the church that determined that those works are inerrant, itself inerrant?
If so, then that isn’t Protestantism. And if not, then you have no inerrant basis for knowing that the texts chosen for inclusion in your canon of Scripture are inerrant.