Power Loader: Has like older brothers who all had muscle quirks and became famous heroes, but he was the youngest and felt very weak. Luckily, he stayed motivated and became a hero.
Midnight: Her parents didn't give her a lot of attention and when they did, they were very abusive. Seeking attention, she became... this.
Present Mic: After he hurt his parent's ear after being born, they started to hate him. They would abuse him often.
Aizawa: His Father was very abusive so he became the Dadzawa we know (and obsess over).
Hound Dog: He grew up on in the discriminatory part of his town and was bullied for being a dog. That motivated him to become a hero.
Snipe: He got rejected by his middle school crush because he was "too weak". He trained so hard that he got scouted and he decided to become a hero.
We all know All Might's backstory pretty well and I don't feel like writing...
Nezu: Was a lab experiment once he was discovered to have a quirk. He was saved by heroes which is why he teaches them. He is still scared of needles.
Ectoplasm: He had a tough time in school and was surprisingly good at sports. He was bullied a lot and called stupid so he decided to teach (and still be a hero). He hated math.
