One possible reason could be that in the fanfic, his parents might be depicted as having made some big mistakes in the past that directly affected Harry in a negative way. For example, they could have made a deal with a dark force that put Harry in danger later on.
In the fanfic, it could be that Harry discovers some dark secrets about his parents. Maybe they were not as noble as they were made out to be in the original story. They could have had some ulterior motives for their actions that when Harry finds out, he begins to despise them.
Well, in the original story, Harry's parents are seen as heroes. But in this fanfic, the whole dynamic is flipped. It's a big deviation as it changes the fundamental view of his parents.
Maybe they were forced into it by some dark magic or a powerful dark wizard. They could have been blackmailed into betraying Harry to save their own lives or the lives of others they cared about.
One possible reason could be that in the fanfic, the author might twist the story to make it seem like his parents' actions had unforeseen consequences that affected Harry negatively. For example, their fight against Voldemort led to Harry being an orphan and having to bear a great burden from a young age.
In some fanfics, they might abandon Harry because they are under a dark spell. This spell could make them lose their love for him and force them to leave. Another reason could be that they are blackmailed by some powerful dark forces. These forces may threaten their lives if they don't abandon Harry.
One possible reason could be to explore different parenting styles in the wizarding world. Spanking, although a controversial form of discipline, might be used by some writers to show how Harry's parents could have dealt with difficult situations. Another reason might be for shock value or to create a unique and unexpected story within the familiar Harry Potter setting. It could also be a way for the writer to delve deeper into the characters' personalities and how they might react in a situation that involves discipline.
Maybe he wants more independence. In many fanfics, characters like Harry might feel restricted at home and long for the freedom to make their own choices, so that could be a reason for him to move out.
Well, some writers might be interested in exploring alternate timelines or universes. In a different reality, they might think that Harry could be influenced by dark forces in such a way that he would do something as horrible as killing his parents. It could also be a form of creative rebellion against the established story. They want to break the rules and see where it takes them. And maybe, for some, it's a way to deal with complex psychological concepts, like how a person can lose their moral compass completely.
Another reason could be that they had some sort of premonition or prophecy that indicated the Dursleys' place was a crucial part of Harry's future protection. Maybe a seer told them that for Harry to grow into the wizard he needs to be, he has to endure the Dursley experience first.
One possible reason could be that he discovers a dark secret about his family. Maybe he finds out that his parents were involved in something dangerous or unethical in the wizarding world, and he can't bear to be associated with it, so he runs away.
One possible reason could be that the fanfiction misrepresents the true essence of Konoha. Naruto has a deep connection to Konoha, and if the fanfiction distorts its values, he might despise it.