It was called Twitter because that's the word used to describe the chirping of birds, which neatly captures the essence of the site.
It's worth remembering, though, that the word "twit" evolved to become a widely-used expression to descibe a foolish, annoying or silly person. This also stems from the real definition of twitter (we've all met people who constantly "chirp" and prattle without actually saying much of value, right?).
Now, there may be a lot of dross on Twitter, but I can see why Jack Dorsey et al might have steered clear from branding those 140-character comments as idiotic from the get-go. "Tweet" was definitely the right call.