Having been brought up (i.e. indoctrinated) as a Christian, I know much more about Christianity than about other major religions, like Islam or Judaism. I will therefore use Christianity as an example, but I’m fairly confident that the case that I make can be made very similarly for other religions.
Any rational person, not necessarily atheist, but at least not indoctrinated with Christianity, when confronted with the Bible, will first note that it’s just a book, written over a long period of time by lots of people, but still just a book nevertheless. Upon reading it he’ll discover that it’s chock full of contradictions and falsehoods, so it might possibly make for some nice and a few not so nice bedtime stories, but it’s certainly not a book worthy of basing ones life on.
The Christian has a different approach. He knows the bible is the word of god. God does not contradict himself, nor does he spread falsehoods, so the christian would seem to be in a bit of trouble when confronted with them, but of course he is not.
You can point out a contradiction to him, like the completely different genealogies of Jesus in the gospels, and he will twist the words as long as it takes for the contradiction to vanish, because, obviously, they need to be twisted, because the bible does not contradict itself.
You can point out to him that the story of creation put forth by the bible is so at odds with what science has found out that it’s not even funny. He will, depending on which christian sect he belongs to, either tell you that genesis is not meant to be taken literally and is just symbolic, i.e. a story, or that it is meant to be taken literally and is, in fact, true. God created the universe a few thousand years ago, but made it look like it was billions of years old. He will point out that there are holes in the fossil record which biology cannot explain. Of course, what he cannot explain is why god would want to fake such an old universe, but then put in those holes.
He does not have to explain, however. God works in mysterious ways and whatever he does makes some kind of sense, even if we cannot understand it.
The christian is thus equipped with a vast array of weapons to destroy any problems that reality lays in the bible’s path. He can twist words, he can declare passages to be just symbolic, he can declare reality to be a fake and even if that doesn’t work out, he can declare that it doesn’t have to, but that it makes sense nonetheless.
He does all these things because he knows that the bible is true. This knowledge is stronger than any fact or logic, so trying to convince him of the contrary will not work.