"Why is Batman, Batman?"
Translation: Hey Batman, why is Batman?
Only Batman can answer that.
Now, if you meant to ask "Why, is Batman Batman?" -- as in, "Can anyone tell me why Batman has taken the role of Batman?", that's a different question. Equally, is the question "What makes the Batman the Batman -- not so much why he adopts the role of batman, but the more philosophical question of why is he who he is.
Then again, there is the comic book answer: because the cave was not filled with opossums.
Why am I watching a Hercules movie with Kevin Sorbo that looks like an extended TV episode? I mean I have much better things to spend my time on, so why?