It could.
Those are really the only two choices? Let me suggest two others. Parts of the bible are true and parts are not. Or, the true nature of reality contains contradictions.
There is a real, and I think unavoidable, philosophical flaw in any argument to reject the bible based on contradictions it contains. The argument contains the following essentials: the bible contains contradictions; since reality does not permit contradictions, the bible cannot accurately describe reality; therefore, the bible ought to be rejected.
This misses two points, one minor and one major. First, there is no automatic reason to suppose that a particular contradictory account is in general less accurate than any non-contradictory account. Contradiction in and of itself is not a cause for rejection. Second, rejection is contingent on reality not allowing a contradiction.
I don’t think that question is yet settled satisfactorily. Relativity tells us that there are no priveleged reference frames. An object can be (for instance) both contracting along its direction of motion and not contracting in that direction. Quantum physics suggests that a particle can both be in a particular position and not be in that same position. Again, I won’t claim that this is the true nature of reality; but the question is certainly not settled. It might be the case that reality is pervasively contradictory.
You cannot compel rejection of the bible, unless you also insist on rejection or non-standard (i.e. kooky) interpretation of the last 100 years of science.
Besides the philosophical fallacy, there are also three particular logical fallacies often committed. Two are avoidable, the third is problematic.
First, there is a misunderstanding of logical conjunction. If the bible is validly interpreted as a conjunction of propositions, each of which has a logical truth value independent of the others (required for the program of rejection by contradiction), then the entire conjunction fails if any of the propositions is shown to be false. If we adopt classical logic, then the law of non-contradiction holds, and a contradiction implies at least one falsehood. Thus, a biblical contradiction causes us to reject the entire bible.
The flaw is in the interpretation of “entire”. We are not logically committed to reject every single thing in the bible. The falsehood of a conjunct does not compel rejection of any other proposition that happens to be related only by the conjunction. That is, if I claim “God exists AND God does not exist AND St. Paul is the capital of Minnesota”, you are not required to reject “St. Paul is the capital of Minnesota”. There is no automatic reason to suppose that falsehood of a proposition pollutes other propositions. The only reason is when, as you’ve done above, you insist that it be the case.
It is quite reasonable to simply accept all the non-contradictory propositions in the bible, and one half of every pair of contradictions. That is still logically valid. In fact, that is exactly (part of) what we do when we say “I don’t accept the bible as entirely literally true”.
Second, there is a misunderstanding of logical implication. If the bible is validly interpreted as drawing conclusions (how we ought to live) based on premises (propositions contained in the bible), and we find a false premise due to a contradiction (or any other reason), then we ought to reject the conclusions.
Logic doesn’t say anything of the sort. If we find a false premise, we are not compelled to accept the conclusions, but there is also no compulsion to reject them. If I claim: “if George was born in Minnesota, then he is a US citizen”, and you demonstrate that George was born in California, you are not required to conclude that he is not a US citizen. There is no logical sense that a contradiction in the bible should cause me to (for instance) stop believing in God, stop praying, or stop attending church.
Finally, and quite damning, are the very consequences of an insistence on non-contradiction. The intuition is that we ought to reject contradictions because they are, in some way, offensive to logic (I have already argued that they are not offensive to the structure of reality). The reason that classical logic requires non-contradiction is due to the (classical) entailment relation, where certain sets of propositions imply other sets of propositions. In this relation, a contradiction implies everything. Thus, if we want to reject anything at all (which we probably can agree on), then we must reject all contradictions.
It is this sense that the bible is a contradictory theory that is supposed to cause us to reject it. To be concrete, suppose we have two statements:
A = “thou shalt not kill”
~A = “whoever strikes someone so that he dies must surely be put to death”
And we claim that one is the logical negation of the other. Then, any theory containing both these statements can be used to derive anything, and must be rejected as a theory.
However, non-contradiction carries with it the law of the excluded middle. In classical logic, the law of non-contradiction and the law of the excluded middle are equivalent: you must either accept both of them or reject both of them. A very weak case can be made for accepting the law of the excluded middle and rejecting non-contradiction. The opposite (accepting non-contradiction, rejecting excluded middle) leads to a contradiction itself, and you cannot both accept non-contradiction and a contradiction. Anyway, insistence on non-contradiction requires insistence on excluded middles.
That is, in the example above, it must be the case that either A or ~A is true. You cannot insist on rejection of the bible on these grounds, without being forced to insist on the validity of exactly half of each pair of contradictory statements in the bible.
And I don’t think you want to do that. You have two choices. You can insist that the two statements above (for instance) are somehow not a pair of a proposition and its negation. That is what we do when we “interpret” the bible. For instance, when we see “thou shall not kill”, followed in the next chapter by a list of times when you should “put [someone] to death”, we should ask if “killing” and “putting to death” are really the same thing, or if one of them is an exception to the rule of the other, or if there is some deontic reading (as things we “ought” to do but are sometimes “required” to violate).
Or, you can insist on some third possibility to A and ~A (like “God does not exist”, or “God never said either of those”). That is, you can reject the law of the excluded middle and thereby accept contradictions. You can reject classical logic (and I think you should, on the grounds that it has nothing to do with the world), which has two consequences. The appearance of contradictions in the bible no longer compels anything. We can tolerate the contradiction. It just might be the case that God embodies a paradox, or commands us to do contradictory things (he’s pretty demanding 
). And, we are no longer forced into your false choices (“accept this interpretation of the bible, or reject the entire thing”).
I guess I’m just stunned at the philosophical program of discrediting the bible. Until we have established that the world is straightforward and meant ot be understood by all, we cannot reject the bible on those grounds as “inaccurate”. Perhaps its accuracy comes at this expense. This idea is the intellectual older brother of fundamentalism. Both insist, at their core, that the bible can only be “all or nothing”, and that any contradiction is fatal.
Consistency is not all its cracked up to be. And a foolish consistency is just that: foolish. If you’re interested in pursuing the hobgoblin of little minds, then there you have it. If you’re interested in truth, you have to be more sophisticated.
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