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I know this is probably bait, but I have nothing better to do right now.
Besides Charizard, he's the powerful badass that was needed during the first generation to draw older gamers in. You had your cutesy shit going on with Clefairy and Jigglypuff and Pikachu, which would get the attention of the young kids...it was the first movie that clinched things for many players.
While there are better storylines in other shows and animes than Mewtwo's, Mewtwo's is as close to "deep" as they were willing to get - the Japanese version doing a bit better but it's not like you needed to be writing Shakespeare to impress 14-18 year olds.
Mewtwo's also one of the few instances where you fight an endboss in the game, can recruit him, and he's just as much of a badass when you're using him as he was when you fought against him, as opposed to the "fight boss with 10,000 HP, boss joins party, now has 300 HP" bullshit you might see elsewhere.
tl;dr; Mewtwo was at least partially responsible for a good chunk of the older players who got into Pokemon in Gen 1, most of which are still around playing the games today.