I guess they call it TWITTER because twits tweet? Seems to me the owner/creator could have thought of a less insulting word. Do you?

TWITTER
To utter a succession of small tremulous sounds as a bird. To talk lightly and rapidly, esp. of trivial matters, chatter. To titter giggle.  To tremble with excitement or the like. Be in flutter.

TWIT
An insignificant or bothersome person

TWEET
A weak chirping sound as of a young or small bird