Keigo Midoryia--formerly Keigo Takami--helped Izuku find his mother after he wandered. Inko took him in upon seeing the state he was in. Manga spoilers to an extent Not necessarily All Might safe here. The road to hell is paved with good intentions. The man sucks as a teacher and is a useless mentor and a dumb hero. I said what I said and I do not take criticism. If for some reason you don't get my dislike of the man, it shall be laid out before you in the following fanfiction.