I'm going off memory here, so there may be flaws.
The full version of the movie explained why Mewtwo fought. Remember the jungle and lab at the beginning of the film? In that lab, there were clones of other pokemon, and a human girl (the daughter of the guy who talked about not wanting the most powerful pokemon etc.). During the cloning process Mewtwo, still young, connected with the girl and she talked to him about her life and such, but she disappeared (can't remember why). Because of this, Mewtwo became unstable and wanted to learn the secrets about life and yadda yadda that he went on about in the rest of the film.
It's on youtube somewhere.