The funny thing about inerrancy is that it really requires several things to be true:
1). The group that selected the Bible must have been inerrant. The trustworthiness of the Bible is only as trustworthy as the group that selected the books. Unless someone wants to join the Church, it fails the test there, but the Church doesn' t make that claim about Scripture
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2). It should have been transmitted flawlessly. This is not true. There are textual variants within it.
3). If it hasn't been transmitted flawlessly, then there must be an inerrant means of determining the textual variants. No such means exists.
4). It becomes irrelevant in translation unless translations are also inerrant. If translations are not, nobody can have an inerrant Bible unless they read Greek, Hebrew, and Aramaic.
5). Even if the Bible were inerrant, it only functions as such as long as its interpreter is as well. We know, though, that people read it in a variety of ways, so the inerrancy fails at the person...and if people could be inerrant, it removes all need for an inerrant Bible.
If one opts out of point #1, then one must explain why the decision on the contents of Scripture was inerrant while simultaneously rejecting the notably Orthodox and Catholic nature of the men who selected it. It becomes a bit of cherry-picking without such a principle.
If one opts out of point #2 by saying that only the originals were inerrant, but not the copies, then the entire issue becomes theologically moot. God did not see fit to preserve an inerrant Bible, so it has no bearing on our lives or the inspiration of Scripture. There is no point even wasting breath on it.
If one opts out of point #3 by saying that God chose certain men to select the text inerrantly, then we are back to the principles of point #1. Why not accept all their theological beliefs without picking and choosing what is often arbitrary decisions on the biblical texts? If their decisions on which text is valid is inerrant, and they claim not to be inerrant in their decisions, then is their claim not to be inerrant also inerrant?
If one opts out of #4, then one needs to explain the same problem as the preceding if there is not total agreement with the theology of the translators (which will come through in translation), and the same difficulty for any claims about not having inerrancy arises (the KJV translators, for instance, felt the need to footnote other translations where they thought they might not be adequately representing it).
If one opts out of #5 by saying that the Spirit will guide the individual if they simply open their heart, then people must either say that the Spirit hasn't led them, and thus, they aren't open to Christ which calls the doctrine of inerrancy into question, they must assert they understand it where everybody who disagrees is somehow dishonest, or that it is impossible to have any reliable interpretation because we cannot know which surrenders inerrancy in its turn. No other means of interpreting can even hope to offer an inerrant interpretation.
In the end, inerrancy cannot be sustained from either Scripture or Christian Tradition, and is utlimately self-defeating.