All Might never intended to take in a child. He’s too busy being a hero to have another human under his care. But what was he supposed to do when he saw a kid with big bright eyes staring at him from the ruins of a building? He couldn’t just leave you. Whoever you were being taken care of by was no doubt dead.
So he scooped you up and took you. And then he continued the job of raising you in your lost guardian’s place. Originally he had just planned for a few days; until he could find somewhere for you to go. Though pretty soon those days turned to weeks, weeks to months, months to years. It’s far too late to just give you up at this point. You’ve got a whole bunch of stuff that no one is gonna use if you go. He may or may not have spoiled you a bit. He may or may not still do so.
And he likes the company. Beats being alone all the time.