>>23290328There is a difference between the anime and the games. Giovanni had nothing to do with in the games, nor did Team Rocket. It was just Mr. Fuji and a group of scientists whose entire goal was to create the perfect pokemon, a genetic clone of Mew, the seemingly most rare Pokemon.
Mewtwo is one of the few Pokemon barring the God levels that has no equal as far as the lore goes. It makes more sense for him to do so in this scenario and concept to do it out of entertainment and combat to give himself an equal, to challenge himself, as opposed to wanting to stop war.
That and considering that for as long as Mewtwo has seemingly existed there hasn't been a war. We have no idea of knowing if Mewtwo was created before or during the war Lt. Surge is mentioned in or not, and assuming he is, it's likely he's been in Cerulean Cave the entire time, awaiting something to challenge him. It's his whole purpose for being there, to be challenged.