This is a critically important question to my Christian friends, and probably of no interest to any other readers - many of whom may just (falsely) assume that it is obvious why genuine Christian beliefs are wrong, or most likely do not even have a clear idea of what genuine Christian beliefs are.
By Christian, I refer to systems of belief in which the Bible is considered the holy, inspired Word of God (for some specific meaning of "Holy", "Inspired", "Word" and "God"....) and is the supreme source of authority on religious matters. This includes most but not all people in the world who would self-describe as Christian - I think its fair to say all mainstream Catholic, Protestant and Orthodox denominations subscribe to the notion, although that core idea manifests in different ways. Protestants might argue that Catholic and Orthodox churches don't believe this, but I'd tend to say they just add more qualifiers. You could also pick other standards for what qualifies someone as Christian, e.g. belief in the Nicene creed. This is all tangential to my argument.
Suffice to say, there are a lot of reasons why I don't personally consider it possible that the whole Bible can be the inspired word of God. Some of my arguments are better than others. The shortest, most succinct "knockdown" objection, though, which rests mainly on the Bible itself and very little that's controversial about either the text or the world, is most succinctly stated in 1 Corinthians 15:21-22 (NIV):
For since death came through a man, the resurrection of the dead comes also through a man. For as in Adam all die, so in Christ all will be made alive.The surrounding verses shed more light on this passage, and another take on the same line of reasoning appears in Romans 5:12-19.
We can blame these versus for the whole doctrine of Original Sin. While I don't think we can say with certainty that Paul believes in Original Sin in the sense a lot of theologians over the centuries have framed the idea, what is clear is that he is drawing a parallel between one man, Adam, bringing Sin into the world, and one man, Christ, sending Sin out of the world (first through the resurrection and then ultimately through the second coming.)
So an honest "biblical" Christian has a limited number of positions to take.
1. Adam was a real person, Christ was a real person. This is a perfectly consistent view to take of the Bible, makes the most sense of Paul's theology, is the most plausible explanation of what Paul himself likely believed, and is very popular in America and several other cultures (such as 15th century Christendom.) Sadly, in other places, where science is taken remotely seriously, it is impossible to defend this view. While you might be able to get a scientist to concede that its a theoretical possibility that homo sapiens sapiens once got to a single fertile couple population bottle neck, it's "only on the strictly philosophical grounds that few things are impossible" kinda point. Actual probability, close enough to zero to round down. And certainly even then this couple could not have been the first two homo sapiens (partly because that the idea doesn't even really make any sense. Evolution is essentially a continuum with only the apperance of discrete groupings any larger than the organism due to sampling.)
2. Adam is a metaphor, Christ is a metaphor. Completely solves the objection contained in 1. Leads to Gnosticism, or Thomas Jefferson style Deism, or some other similar historical Christian heresy. Many of these have some intellectual appeal, but are so different from mainstream modern belief as to justifiably not be called Christian, because they force you to completely change the reading of the entire New Testament. Christians have spent centuries generating solid arguments to try and knock down any possiblility of holding this view, for good reason.
3. Adam is a metaphor, Christ is a real person. And Paul is Satan. Or smoking crack, because this reading is only possible if Paul is insane or evil or a con artist or something else which completely undermines any authority he has on these topics and demands that we tear all his writings out of the Bible (which is all fine and holy except for Paul's bits, of course). This is a bit of a shame, because Paul is the intellectual father of Christian theology. Without Paul we might still have a religion which could perhaps be called Christianity, but while it wouldn't be as radically different as what case 2 would imply, it would still be radically different enough that this remains a losing move for a Christian to make in this particular exchange. It also brings up the interesting and painful question of what parts of the Bible we can then trust, and on what grounds. The end result of such a process occuring after the initial concession is not a pretty sight.
4. Some crazy compatiblistic compromise that tries to iron out one of the difficulties raised above. I made up one of these while committed to a psych ward. It was kind of a cross between 2 and 3. One day I might try to explain it coherently and sanely to someone in full, but I think it might be a little tricky to do so.
5. The Bible has serious flaws and is therefore not "inspired" - maybe parts of it are, but we can't reliably tell which parts. Therefore, by contradiction, Q.E.D., etc.
There is something critical about the argument I have made above that distinguishes it from other issues, like minor factual inconsistencies (how did Judas die?), bickering about translations or correct reading ("this passage is a poem of course you shouldn't expect it to be scientifically accurate"), historical doubts (Exodus doesn't exactly match other sources we have), and so forth; these all make Christiantiy less likely, to varying degrees, but this is far worse than just "less likely". It pushes the Bible beyond Inerrant, beyond Infallible, and indeed beyond Inspired. You have to go down the path of either full blown anti-science Creationism, or almost complete rejection of a core Christian doctrine. Or you must indulge in what I think amounts to massive intellectual dishonesty in your Bible reading, the kind that so offends Christians when ignorant atheists (or heretics) try to pull it off.
I've never come across a convincing escape route out of this particular flanking manouver (except, as noted, during the time when I was at my craziest.) The apologist appears surrounded on all sides with no way out. I could, of course, be wrong. But I think its far more likely Paul is the mistaken one here, and I can't see how Christians have any legitimate tactic left but to quote something like 1 Corinthians 3:19, and thus win their battle but concede mine.
Which, of course, means they ultimately have lost the war for my soul - supposedly the one that counts. Or maybe they haven't. But that's another one of my crazy heretical theories that can wait for another time.