Sweet Lullabies

Izuku was at the delicate and fragile age of four when his life began moving downhill. He was diagnosed quirkless by nearly every doctor in Mustafu, Japan. There was one, however, that gave him hope. He had said that Izuku had a dormant quirk, one that needed to be activated. Little four-year-old Izuku learned just how cruel the world was.
After Izuku's mother told him that his father was dead, she pushed him harder and harder to activate the quirk. She lost hope with him fast and tossed him away like he was naught more than trash.

After making it into class 1-A of the hero course at UA, Izuku's life just keeps going downhill.