"You either die a hero, or you live long enough to see yourself become the villain." Or, you're raised a villain, rebel when you're nine, and fight against the odds to become a hero anyway. That's how it is in Izuku's case.

“Midoriya also wants to go to Yuuei.” At this statement, Izuku’s classmates mocked him and on any other day, he would have taken it. But getting hit with a quirk while watching a villain fight before school changes the scenario. In which Izuku’s class learns you don’t need a quirk to take someone down a peg.