Well, it could be that Snape framed Harry for something serious, causing him to be expelled and leave Hogwarts. Maybe it was a misunderstanding or a plot by Snape to get rid of Harry for some reason related to their past conflicts.
One possibility is that Snape discovered Harry was involved in a forbidden magic practice and insisted on his leaving. Or perhaps Snape had a personal vendetta against Harry and used his authority to force him out of the school.
In some fanfictions, it might be because Snape exposed a secret of Harry's that led to his departure.
It could also be that Snape represents everything that Harry hates about Hogwarts at that moment in the fanfiction. Snape's strictness, his partiality towards certain students, and his general unfriendly attitude might make Harry feel that Hogwarts is no longer the safe haven it once was. So, he leaves, thinking that he can find a better place where he doesn't have to deal with Snape's negative presence.
In some fanfictions, Harry might leave because of Ginny due to a misunderstanding. For example, he could misinterpret Ginny's actions or words as a sign that she no longer loves him or wants him around. This could be something as simple as seeing her chatting happily with another guy and jumping to the wrong conclusion.
One possible reason in fanfiction could be that Snape's constant bullying and unfair treatment finally pushed Harry over the edge. Harry might have felt that he couldn't take it anymore, especially if Snape made his life at Hogwarts unbearable in ways that the other teachers didn't notice or couldn't stop.
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 that he feels he has fulfilled his purpose there. Maybe he has achieved certain goals related to protecting Harry Potter secretly, and he decides it's time to move on to other things. For example, in some fanfictions, he might leave to explore his own family history or to further his research on the Dark Arts in a more secluded place.
In fanfiction, one reason could be his desire for a fresh start away from the memories at Hogwarts. Maybe he feels he has done all he can there and wants to explore new magical knowledge elsewhere.
Hogwarts is a well - established and copyrighted world within the official Harry Potter series. Fanfiction often takes creative liberties that might not align with the original concept of Hogwarts as envisioned by J.K. Rowling. So, it's not a proper place for fanfiction in a legal and purist sense.
Because fanfiction is a way to keep the magic of Hogwarts alive. Harry Potter, being the hero of the story, would understand the importance of that magic and want to protect the creative works that continue to explore Hogwarts.
Perhaps he's following a lead related to his parents. There could be some secrets about his family that are hidden in America. He goes there to uncover the truth and learn more about his family's past that might not be available in the UK.
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.