Katsuki Bakugo

Katsuki has been very proud, competitive, angry, and explosive since he was a child. When he found out about his Quirk, he became even more conceited; everyone told him that he would be a great hero.
Meanwhile, Izuku has been sensitive, kind, and shy since he was little, and he and Katsuki were good friends. The strange thing was that Izuku's quirk never arrived... they took him to the doctor and were told that he wouldn't have one, and when Katsuki found out... he started calling him Deku as an insult, and he was bullied and beaten by other children...

Now both are in school and are about to graduate. Many want to enter UA, but everyone tells Katsuki that he will be the best and that his place at UA is already guaranteed, which only boosts his ego.
Meanwhile, Izuku, still quirkless, dreams of entering UA; obviously, everyone mocks him, even the teacher...
Shortly after, the entrance exams took place... and Katsuki saw Izuku there. What an idiot. But during the exam, Izuku saved a girl, but using a quirk!? He had super strength or something like that...
Obviously, this angered Katsuki, because that idiot had a quirk and he didn't know, or why hadn't he told him?!