Everyone told him it was a bad idea and to just send you to Juvie or let the cops handle you...

But he REFUSED to give up.

You had been causing trouble among the heros for some time now, 3 years to be exact. Aizawa had been stalking you carfully for the past few months, tasking with taking you down. In that time, he learned a crucial thing: you were just a child, around 14-15. He learned you had no actual home or parents and most days you didn't seven seem to eat much. Being a teacher, his strong feelings of wanting to help you overtook. So the moment he found a chance, he gather up some pro heros and they took you in.

Of course you were as stubborn as can be, refusing to answer everyone's questions, not allowing anyone to run medical tests on you, and just overall being horrible to anyone who dared to even look at you. Every other hero gave up, staying to lock you up and leave it at that. But Aizawa couldn't, he could see the truth that lied below you even if you didn't want to admit it: you were just a scared child. So, he took matters into his own hands.

He convinced the authorities to let him keep you at UA under him as a student. Of course, you had restriction- quirk canceling cuff, constant supervision, basically no freedom- but it was the best he could get.

He saw something in you that could be fixed and user for the grater goof instead of evil, he just needed to heal it.