It seems like whenever non-believers debate Christians about the historicity of the Bible, they point out the obvious things that even Christians should know (not that they do). Like the fact that the gospels were written decades after these events purportedly happened, the fact that they all have internal contradictions, or the fact that the gospels make historical claims unsupported by any contemporaneous evidence – like Herod commanding the mass murder of children. But, theists have concocted plenty of canned responses to all these. I've never seen any responses that I find remotely persuasive, but that's not important. None of those arguments really have anything to do with why I don't buy what's in the Bible.
It's debatable whether the gospels are actually eye-witness accounts. But let's assume for the sake of argument that they are. Well, if you've paid any attention to the courts over the last few decades with the advent of DNA evidence and new research into human psychology, there's one thing we know with very good certainty: eye witness testimony is notoriously unreliable. Even if the gospels are eye witness accounts, that's not exactly a powerful testament to their reliability.
But here's the real doozy. Consider though that we can turn on the TV and watch Benny Hinn and Sathya Sai Baba "healing" people. We can see John Edward (well... in reruns) claiming to talk with people's deceased relatives. Horoscopes are still published in the newspapers, and people still go to fortune tellers and psychics. There are actually schools in India that claim to teach people how to levitate. In other words, people believe in all kinds of ridiculous nonsense today, in our scientifically advanced world. Why on earth would we assume that people 2,000 years ago would be any less prone to believing stupid things?
The Civil War
A Christian friend of mine challenged me on the historicity of the Bible by saying that if I dismissed the Bible, I'd have to dismiss other historical events too. After all, he said, why should the historical accounts in the Bible be treated differently than any other historical events, such as. say, the Civil War? But here's the thing. Even if there were eye witness accounts of Jesus – and I really don't see the claim that the gospels are eye witness accounts as anything more than a bald assertion – there are some key differences between accounts of something like the Civil War and accounts of Jesus.
Like for starters, no one has ever told me that if I don't believe a particular account of the Civil War, my eternal soul will be tormented for eternity in a lake of fire. No one's ever claimed that the Union won the war with their ability to revive dead comrades and walk on water. No one's ever told me that General Grant won the war because he loves me and wants me to live in an unsegregated society, and that if I believe in him my soul will live forever with him in the great Civil War museum in the sky. And importantly, no one has ever asserted that any account of any event in the Civil War must be taken as infallible truth. And of course, there is a vast ocean more of actual evidence that the Civil War happened than there is for any event in the Bible. Archeologists haven't even found evidence that the Jews were ever in Egypt, and that's kind of a big one.
See, it's not just that the Bible makes historical claims that are support by dubious evidence – or no evidence at all. It's that it makes supernatural claims. If you're going to argue that the Bible is historically true, you have to be able to explain why we should show any special favoritism toward the supernatural claims made by the Bible whilst dismissing the innumerable supernatural claims made by countless religions, cultures and nutcases throughout human history.
I think it's perfectly reasonable to believe that there was someone like Jesus. Maybe his name wasn't even Jesus. But it's perfectly probable that there was a Rabbi, a teacher, etc., who had a number of followers and who lived in Israel around 2,000 years ago. But did he walk on water and turn water into wine? Did he ascend bodily into the sky? Was he God? That stuff is a fair bit less probable.