Jesus vs Paul Bunyan
If I were to say that the claims for Jesus are just like claims for Paul Bunyan, you might become upset. You'd probably argue that serious claims for Paul Bunyan's existence are ridiculous, or that no one really believes in Paul Bunyan, and that the comparison is unfair for these reasons alone.
But notice that none of these complaints are actually rational arguments against Paul Bunyan. Arguing that a claim is false because it is ridiculous is a logical fallacy known as an "appeal to ridicule.' We all know examples of claims that appeared ridiculous but were actually true, it was once ridiculous to suppose that man could fly. Arguing that a belief is true or false based on its popularity is also a logical fallacy, known as 'ad populum'. Again, we can all think of popular claims that were shown to be false, such as the idea that the earth was the center of the solar system.
So when we rule out Paul Bunyan as a real person, how do we really come to this conclusion logically?
We do so mainly through two means: by citing a lack of reasons to hold to the belief, and by citing how the claim violates what we do know of the world. We know that there are no good reasons to believe that Paul Bunyan really existed. There's no evidence that such a man existed, despite the fact that such a giant would have been an incredibly noteworthy individual. At the same time, we know claims for Paul Bunyan violate what we know of the world, and claims that ask us to contradict what we already know of the world requires extraordinary evidence:
As David Hume wrote in An Enquiry Concerning the Human Understanding:
[A] weaker evidence can never destroy a stronger... [N]o testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavors to establish. (Enquiry X)
Hume saw that since the laws of nature are based on literally trillions of observations by billions of people over thousands of years, second hand testimony of miraculous violations of these laws were likely to be false.
So what happens when we apply how we really rule out Paul Bunyan claims to Jesus claims? The exact same problems arise: there's no evidence to support an actual 'Jesus', despite the incredible effect such a divine being would have had on his times. And "Jesus" claims violate what we know of the world.
So, when we are consistent we find that there is no rational difference in the claims.
How about a human Paul Bunyan?
A very avid Bunyan-ite might want to find away around these insurmountable problems by making a more humble claim for Paul. So imagine that I am now claiming that Paul Bunyan did exist, but that he was actually a French Canadian logger, called 'Paul Bonjean'. He was not over 100 feet tall and able to knock down a swath of trees with one swing...
...but he was a big guy who could knock down a tree quicker than any other lumberjack around.
Now that I have watered down my claim to something within the bounds of nature, would you agree that "Paul Bunyan" was real? Probably not, because you sense you were a victim of a 'bait and switch'. This "Paul" that you are being given is no longer 100 feet tall, no longer a man of myth. You'd argue that a "human Paul Bunyan" is an oxymoron - Paul Bunyan, by defintion, is something more than just human. Finding a human Paul Bunyan as the origin of the legend proves that the legend is myth.
Jesus vs Paul Bunyan
So, let's now apply this all to "Jesus" claims. It turns out that Jesus claims are in fact just like Paul Bunyan claims when we look at the situation rationally. There's no good reason to believe either claim and both violate what we know of the world. And interestingly enough, just as the attempt to 'salvage' Paul Bunyan as a 'man who inspired the legend' actually demonstrates that really isn't a Paul Bunyan, the same situation holds true for "Jesus".... Jesus as a a man who inspires the legend is no more "Jesus the Christ" than a tall guy with an axe is "Paul Bunyan."
Those who know the good, do the good. - Socrates