Oh for godsake!
Can we start at the beginning?
Why were the accounts written at all?
Was it with the express intent that people should later look at these writings and say "yup, they agree" or "yup, they disagree"? This similarly undermines the suggestion that it was entirely a work of fiction, because if it were they would surely have gone for some kind of character continuity (after all, JK Rowling can manage it)?
Surely they are ancient diaries (amongst a few others), that are written subjectively?
As for why those four became part of the canon we call "The Bible", today? Well Narkissos suggested a reason for that.
What's to believe or not believe?
Do we cast out all the compiled wisdom of the Encyclopaedia Brittanica because of typesetting mistakes? Nope.
Why, then, do some have an all-or-nothing view of a compilation of diaries?
Does it become a Holy Grail of critical thinking to be able to declare that an individual mentally debunks the whole lot? Have we totally lost our ability to be eclectic?
Personally I love the Gospel of John, and the letters attributed to an author of the same name.
That having been said, the Sermon of the Mount (in Matthew) is a masterpiece of literary thought.
Yet they both contain wildly different messages, albeit retaining the same central character.
A few words to the wise...