I think it's because Lisp was born out of, and maintains the spirit of the hacker culture. The hacker culture is to to take something and make it "better" according to your belief in "better".
So when you have a bunch of opinionated hackers and a culture of modification, fragmentation happens. You get Scheme, Common Lisp, ELISP, Arc. These are all pretty different languages, but they're all "Lisp" at the same time.
Now why is the community fragmented? Well, I'll blame time and maturity on that. The language is 50 years old! :-)
