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.
Well, it could completely disrupt the relationships. For instance, his friendship with Ron and Hermione might be strained as they try to convince him to stay. This is different from the original where they are all united in their Hogwarts experience.
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 he's tired of the constant danger at Hogwarts. There are always threats like Voldemort's followers or dark creatures lurking around. Another reason might be that he feels pressured by the expectations placed on him as 'the Chosen One'. Everyone expects him to save the day all the time, and it's a huge burden.
The teachers would also be concerned. Dumbledore might try to have a deep conversation with Harry to understand his motives. Some teachers might see it as a sign of weakness or that they have failed in some way to make Hogwarts a comfortable place for Harry. As for his enemies, they might see it as an opportunity to strike while he's vulnerable.
In the fanfic, Harry Potter could meet the new generation of students. They would be in awe of him. He might also encounter some of the ghosts, like Nearly Headless Nick, who would surely have some interesting stories to share since Harry left. And there's a good chance he'll meet the caretaker, who would probably give him a hard time about coming back and causing a stir. Moreover, he could cross paths with some of the older students who idolize him and want to learn from his experiences.
It might be significant as it shows the deep engagement of fans with the Hogwarts setting. By reading fanfic set in Hogwarts, they can further immerse themselves in the magical world, experiencing different scenarios, relationships, and adventures that are created by fellow fans.
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.
Well, in some fanfics, the idea that Hogwarts is a horrible school might come from a different perspective. Maybe the author wants to explore the dark side of the school that wasn't fully shown in the original books. For example, the strict rules could be seen as overly oppressive to some characters in the fanfic.