pyromania

Having lost his mother when he was four and deemed quirkless at five, Izuku Midoriya wasn't gifted a good childhood. He grew up in less than caring foster homes, tossed from place to place like an unwanted animal, rarely staying in one home for more than a month.

When he turns seven, his quirk manifests. He's left to fend for himself when his foster parents at the time kick him out onto the streets. They didn't get in trouble, saying that he ran away, but didn't mention his gaining a quirk.

They wrote him off as a lost cause as a result.

With that, the poor child is left to try to control a powerful fire quirk all on his own.

So by the time he's eight, he's homeless, has a volatile quirk, and is living in one of the areas that heroes tend to avoid.

Well, not all heroes.