Maybe he needs the money to fund an independent research project. He's always been curious about certain magical phenomena, and withdrawing his money would give him the financial means to pursue that knowledge without relying on Hogwarts or the Ministry.
It could also be that he's trying to help out a friend in need. For example, if a Muggle - born wizard friend is facing financial difficulties due to family issues in the Muggle world, Harry would withdraw his money to assist them.
In the fanfic, Harry might be under a lot of pressure from the wizarding community. Everyone expects so much from him and he might feel suffocated. He could think that leaving Hogwarts and going into hiding or finding his own way to fight against evil without the constraints of school would be a better option. He wants to break free from the constant scrutiny and the pre - defined path that Hogwarts seems to offer him.
In some fanfictions, it might be due to an alternate reality. For example, if there was a different prophecy or a different turn of events at the time Voldemort attacked. Harry could leave his parents to fulfill a new - found destiny in this altered world. Also, it could be because of a miscommunication. A magical misunderstanding might lead Harry to believe he has to leave his parents for their own safety.
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.
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.
One possible reason could be to protect them. In many fanfictions, Harry might believe that by distancing himself from his friends, he can keep them out of danger. For example, if there is a new dark threat targeting him specifically, he may think that the enemy will use his friends against him.
One reason could be to escape the lingering dark magic and the constant reminders of their past battles. Britain, especially Hogwarts, has seen so much turmoil that they might feel the need for a fresh start. Another reason could be to explore the wider wizarding world. They've been mostly centered around Britain in the original stories, and in fanfiction, they could leave to discover new magical cultures and spells in other parts of the world.
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.
One possible reason could be that she is under some sort of dark magic influence. In the wizarding world, dark magic can manipulate people's minds and actions. Maybe she was imperiused by a Death Eater or some other dark wizard who wanted to get to Harry through her. Another reason could be that she has been hiding a deep - seated jealousy. Perhaps she is jealous of Harry's fame and the attention he gets from everyone, including other girls, which could lead to her betraying him out of spite.
It could also be due to a choice Harry makes that his friends don't agree with. Suppose Harry decides to take on a very dangerous mission alone to protect his friends, but they see it as him not trusting them. This could lead to a rift and eventually him losing their friendship.