I'm pretty new here, but I thought I'd throw out my idea anyway.
20 years ago, Team Galactic released a legendary pokemon in order to control the world. However, a child appeared to try to stop them. Seeming to follow in the footsteps of previous pokemon trainers in Kanto, Johto, and Hoenn who had stopped evil, it was likely that he would succeed.
But, something went wrong.
The trainer was defeated, and the world fell under the control of Team Galactic. None could stop the power of the legendary pokemon.
Today, all of the gyms and the Elite 4 have been disbanded. You live in a small town which has only been slightly affected by the new world rulers.
Its been years since your father disappeared after a Galactic "investigation" group visited. Your mother tells you that your father worked for a resistance organization, and you want to follow in his footsteps.
So, your mother tells you of the location of a resistance base, the only information she knows about it. However, before you leave, she gives you one of three pokemon, left by your father.
Despite Team Galactic's rule with an iron fist over the world, certain resistances formed from underground organizations, led by none other than Team Rocket.
Yup, Giovanni leads the resistance. Although advanced in age by this point, he is still a very powerful trainer.
So, you begin your journey, joining Team Rocket and the resistance in order to avenge your father, and end Team Galactic's rule.
(I really wish I could hack my own games well)