It could also be that the fanfic might interfere with the way he wants his story to be remembered. His adventures at Hogwarts were real and important to him, and when fanfic changes the narrative, it's like his story is being disrespected. For example, if a fanfic portrays him as cowardly when he was actually brave, that would surely make him dislike it.
Perhaps he hates Hogwarts fanfic because it can create a lot of chaos in terms of the lore of Hogwarts. There are so many fanfics out there with different takes on magic, the houses, and the professors. He has a set understanding of how Hogwarts works, and when fanfics deviate too much from that, it makes him not like them. Also, some fanfics might focus too much on romantic relationships in a way that doesn't feel true to his real experiences at Hogwarts.
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.
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 reason could be that the fanfic distorts the characters he knows well from Gryffindor. For instance, if it changes the personalities of his friends in Gryffindor in a way that doesn't seem right to him.
One possible reason could be that he was under the influence of a powerful dark magic or a curse that made him lose control. Another reason might be that he was tricked into believing Hogwarts was a threat to the wizarding world in some extreme way. Maybe a powerful enemy manipulated him to think that destroying Hogwarts was the only way to save everyone.
It could be that Harry finds out about Dumbledore's secrets regarding the Deathly Hallows. If Harry thinks Dumbledore was more interested in the Hallows for his own purposes rather than for the greater good, it might make him hate Dumbledore.
One reason could be that he doesn't like the spotlight that comes with being a Gryffindor. In the original story, Gryffindors are often in the limelight, and in fanfiction, he might be tired of all the attention.
Maybe he hates it because it often distorts the real story or characters he knows. Fanfics can take the story in wild directions that don't align with his own experiences.
She might hate it because it could change the way people see her character. In the original story, she is a strong and independent person, but fanfiction might portray her in a wrong way.
One reason could be to give him a stronger connection to Hogwarts. As the heir, he might have special privileges or knowledge about the school. Another reason is to add a new dimension to his character. It makes him more than just a student who defeated Voldemort.
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.