A Hero Career Sponsor
Shigaraki Tomura does not need a good reason to do what he wants. Often, the most random desires lead him to the most favorable outcome. In the game of life, it's best to leave no stone unturned, no side quest unfinished. No matter how petty the action, he'll do anything to spite All Might and hero society, even if it includes helping a kid become a hero.
Midoriya Izuku does not see the point in living after being told by his idol to give up on his dreams. Without a quirk, there's no point in existing in a world defined by quirks. But, with a quirk—no matter how suspiciously obtained—he could do everything that was once denied to him. Even if it meant cheating, even if it meant conspiring with villains, he'd to anything to be a hero.
ORShigaraki Tomura meets Midoriya Izuku on a rooftop and hears the story of how All Might crushed his dreams. In his caprice and eagerness to prove All Might wrong in everything, he offers him a quirk upon seven conditions.