My Mewtwo Theory
So we all pretty much guessed that Mewtwo was created by Dr. Fugi(aka Mr. Fugi), and that in the anime Team Rocket funded the project. My the theory is that something similar happens in the GAMES. Now, this may sound a bit Farfetch'd , but hear me out. Team Rocket has some kind of control over every city except Pallet Town, Pewter, Vermilion, Fuschia, and Cinnabar Island. Pallet because there's nothing of importance there. Pewter because they control Mt. Moon. Fuschia probably because Koga easily outclasses them. Same goes for Vermilion. Now we get to Cinnabar. Maybe they don't have any influence over Cinnabar Island is because they once DID. But what does this have to do with Mewtwo? Well, in the post-game, Mewtwo is in Cerulean cave. My theory is that the Team Rocket grunts in Cerulean already know that, and so one's recruiting strong trainers to go in and catch it for them, and the other steals Dig to help against Mewtwo. In Mt. Moon, Team Rocket is stealing Moon Stones to make their Pokémon more able to withstand Mewtwo's attacks. In Lavender Town, they're trying to catch some Ghost Pokémon so they have an advantage over Mewtwo. In Saffron, they try to get their hands on the Master Ball, which would make it much easier to catch such a powerful Pokémon. Mr. Fugi knows how dangerous team Rocket and climbs Pokémon Tower to stop them. And, to top it all off, Cerulean Cave(where Mewtwo resides) and both Team Rocket hideouts(if you want to count FRLG) share the same music. Then again, Bruno's room has that music also. HMMM... but it's just a theory, and reply your thoughts about it