It could be his mother. She might think that UA is the best place for Izuku to become a hero and force him to go there for his own good, even if he has some doubts or hesitations.
Another possibility is that he joins a different hero school. Maybe there's a smaller, more specialized school that focuses on a particular aspect of heroism that UA doesn't. For example, a school that specializes in rescue operations could be a great fit for Izuku's empathetic nature.
He might form closer bonds with local heroes in his neighborhood. Since he's not at UA, he would have more time to interact with the heroes who operate near his home. They could become his mentors or friends, guiding him in his hero journey.
In this kind of fanfiction, Izuku might face a lot of challenges. Maybe he is forced to go to UA by some external power or person against his will. He could struggle to adapt to the new environment at UA, having to deal with difficult classmates or strict teachers. Also, his own self - doubt might intensify as he didn't choose to be there on his own terms.
One reason could be fear. The life of a hero is full of danger. Izuku might have seen the toll it takes on heroes, like All Might's weakened state. He could be afraid of getting seriously injured or even dying. Another reason might be self - doubt. Despite his initial dreams, he may have come to believe that he doesn't have what it takes to be a great hero, in terms of both physical and mental strength.
In some fanfictions, the author might have made Harry not go to the Yule Ball because they want to create a different plotline. Perhaps they are focusing on Harry's independent study or some secret mission that he has to undertake during the time of the ball. So, instead of going to the ball like in the original story, he is off doing something else more important in this fan - created scenario.
Maybe in the fanfiction, Harry has some bad experiences at Hogwarts before. For example, he might have been bullied by some students or had a really tough time with certain teachers. So he doesn't want to go back.
It could be that in this fanfiction, Harry has found a new place outside of Hogwarts that he feels more comfortable in. He might have made new friends or discovered new magic that he can't practice at Hogwarts, so he doesn't want to go there.
The story could focus on Izuku becoming a hero - support figure. Instead of being on the front lines, he could use his intelligence to develop new technologies or strategies for heroes. This would be a different path from the traditional hero - becoming storyline.
One possible storyline could be that Izuku discovers a different quirk within himself. Maybe a latent quirk that was overshadowed by his admiration for All Might and One for All. For example, he could have a quirk related to intelligence amplification, which would make him a brilliant strategist in hero battles.