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.
One possible reason could be that he wants to break away from the pre - determined path. In fanfic, the author might want to explore an alternative version of Harry who is tired of the constant danger and expectations at Hogwarts. He may feel that staying there will only lead to more battles and losses, so he rejects it to seek a normal life.
One possible reason could be that he feels overwhelmed by the constant danger at Hogwarts. In some fanfictions, the threats he faces, like from dark wizards or dark magic within the school, might push him to the point where he thinks leaving is the only way to keep himself and his friends safe.
He might leave Hogwarts in fanfic due to a sense of disillusionment. Maybe he discovers some dark secrets about the school or the wizarding world in general that make him question his place there. It could be something related to the way the school is run or a conspiracy among the teachers that he stumbles upon.
One possible reason could be that the author of the fanfiction wants to explore a different storyline. Maybe they want to show Harry facing challenges outside the familiar Hogwarts environment, like in the wizarding world at large or in Muggle society.
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.
One possible reason could be misinformation spread by the Ministry of Magic. They might have spread false rumors about Harry being a threat, which influenced the Hogwarts community. For example, if the Daily Prophet printed false stories about Harry's supposed dark magic activities, it could turn some students and staff against him.
One possible reason could be that he feels constantly in danger at Hogwarts. With all the dark magic threats and attacks that keep happening, he might think leaving would keep his friends and himself safer. For example, after the Chamber of Secrets incident, he might have considered leaving to protect others from Voldemort's influence.
Perhaps he runs away because he feels misunderstood. In the fanfiction, the other students or even some of the teachers might wrongly accuse him of something. He could be tired of constantly having to defend himself. Like if he was wrongly blamed for a serious incident at Hogwarts, and no one seemed to believe his innocence, he might just leave in frustration.
In some fanfictions, Harry might be expelled for being wrongly accused of using dark magic. Maybe someone framed him by planting dark magic items in his dorm. Another reason could be that he continuously breaks school rules in a way that the school can't tolerate, like sneaking into the Forbidden Forest too many times without permission.
One reason could be that he doesn't like others taking creative liberties with his story. He might feel that it's his story and only the original version should be the 'true' one.