If Quirkless discrimination was a little bit worse, and if Izuku wasn't as forgiving...
Well.
(Featuring: All Might's Absolutely Horrible Teaching™, a slightly more self-aware Izuku, the League Of Villains, very little forgiveness, and a lot of traumatized kids.)
“I’m glad he’s not hurt,” a man’s voice says quietly, “You said you found him in an alley?”
“Yeah,” Present Mic sighs, sounding grave, “But Shouta…it’s like I said. There was a dead dog, for sure dead. Izuku touched it and brought it back to life, just like that.”
Izuku has a quirk that goes against the laws of nature. A target for both villains and heroes alike, he’s rescued as a young child by Eraserhead and Present Mic, raised in secrecy at UA. When he eventually becomes a UA student and his quirk is thrust into the limelight, Izuku must learn how to adapt, or fall.
When his mother dies, Aizawa Shouta takes his brother Izuku to live with him. However, between dealing with the grief and Izuku starting at UA, they don't have much time to spend with their secret family...
...who decide to invade on the third day of school.
Or:
Inko dies, Aizawa and Izuku are brothers (and related to half of the League), Class 1-A finds out about the first half and Tenko is VERY protective of his younger brother.