One day the head of the esteemed crime organization known as Team Rocket decided "HEY FUCK ALL THIS TRAINING POKEMON SHIT LET'S JUST MAKE ONE." And thus Mewtwo was born.
Okay, so the story's more complicated than that. The part about Mewtwo's creation being endorsed by Giovanni of Team Rocket was true, though. A lab was built in a remote location where scientist used DNA from the legendary Pokemon, Mew, to clone a new creature appropriately called Mewtwo. Upon awakening from his "sleep", the Pokemon discovered that should he remain in the lab, he would only be subjected to more experiments, being treated like a project and not a living creature. Enraged that the scientists cared so little for him and that this might be his destiny, he destroyed the entire lab (and the scientists) with his psychic abilites.
It was in the wreckage that he was "found" by Giovanni. The man promised Mewtwo that he would help the Pokemon control his powers and that by doing so, he would learn his true purpose in life. After much rigorous training, Mewtwo became a nearly unstoppable force. However, when he again asked Giovanni what his purpose is, the man responded that the Pokemon's only purpose was to battle for Giovanni and be his tool.
Mewtwo: You said we were partners, we stood as equals. Giovanni: You were created by humans to obey humans. You could never be our equal. Mewtwo:Humans may have created me, but they will never enslave me. This cannot be my destiny. I was not born a pokemon, I was created. And my creators have used and betrayed me. So... I stand alone"
Mewtwo then concluded that all humans are morally corrupt creatures undeserving of the world, and that the Pokemon that were humanity's "friends" were no better. He flew away from Giovanni's gym and resolved to bring a new era: one that would only consist of him and "superior" clones such as himself.
BUT IS THAT ALL?
Well, not quite. But for that, we're going to have to backtrack to before Mewtwo woke up in the lab. We'll have to go back to Mewtwo's origins.