In the fanfiction, it could be that Harry's aunt and uncle managed to intercept the letter before it got to Harry. They were so determined to keep Harry away from the wizarding world that they might have found a way to stop the owl or trick the postal system. They could have used some kind of Muggle - magic repelling charm they got hold of somehow. This would be a very interesting twist in the story as it shows how far they would go to keep Harry ordinary.
One possible reason could be that the owl got lost on its way. Maybe it was attacked by some magical creature or got distracted by a powerful spell. Another reason might be that someone deliberately intercepted the letter. In the wizarding world, there could be dark forces at work who don't want Harry to go to Hogwarts. It could also be a bureaucratic mix - up at Hogwarts itself. Maybe the admissions office made an error in their records and didn't send the letter.
Maybe it's a magical protection. In the wizarding world, there could be some ancient magic associated with hair length. Long hair might act as a sort of shield or a connection to some deeper magic that Harry unknowingly benefits from.
The story could develop in a very different way. Harry might continue to live a normal Muggle life, completely unaware of his magical abilities. He would probably grow up thinking he was just an ordinary boy, going to a normal school and having normal friends.
One possible reason could be the overwhelming burden of his destiny. Constantly facing dark forces and the pressure of saving the wizarding world might have worn him down. Another reason could be the loss of his loved ones. For example, if in the fanfiction Hermione or Ron were killed, that could shatter his spirit.
In some fanfiction, Harry might renounce his name to explore a new identity. He has been through so much as Harry Potter, and by giving up his name, he can break free from the predefined roles and destinies associated with it. He could then embark on a journey of self - discovery, free from the constraints of the name that has both defined and haunted him.
One possible reason could be that in the fanfiction, Harry might have discovered some dark secrets about his parents that made him feel betrayed. For example, if he found out they had some hidden and unethical magical experiments in their past.
In some fanfictions, his family might be involved in dark magic or have a bad reputation. So, Harry Potter refuses them to uphold his own moral values. He is known for his strong sense of right and wrong, and if his family goes against that, he would distance himself.
One possible reason could be that he might feel abandoned. Growing up without them, he could resent the fact that they left him an orphan. He might think that if they were really so great, they would have found a way to survive and be there for him.
Perhaps he discovers some secrets about his parents that he doesn't like. For example, he might find out that they were involved in some dangerous or unethical magic before. This new knowledge could make him angry at them for putting themselves and their family in jeopardy.
One possible reason could be the extreme betrayal he has faced. Maybe some characters he trusted deeply turned out to be working against him in ways that were unforgivable, like revealing secrets that put his life and the lives of his friends in danger.