Perhaps there are some external factors. In the fanfic world, it could be that he has an opportunity elsewhere that requires him to move out. Like he got a great job offer in another place or has a chance to study at a special school far from home, which makes moving out a necessity.
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.
One reason could be that he wants to seek independence. Naruto has always been a bit of an outcast in his family, and he might feel that moving out is a way to prove himself and grow on his own. He could also be tired of the family drama or conflicts that might exist within the family unit in the fanfic.
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.
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.
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.
Maybe he discovers some dark secrets about his family. For example, if his parents were involved in something he considered unethical in the fanfic's plot. It could be that they were part of a group with a hidden and evil agenda.
One possible reason could be a misunderstanding. Maybe he discovers some secrets about his parents that he misinterprets. For example, if he finds out they were involved in some dangerous or morally ambiguous activities in their youth that he doesn't fully understand at first.
One possible reason could be that he discovers some long - hidden family secrets that make him question his parents' actions or decisions. Maybe he finds out about some dark deeds in their past that he can't overlook.
One possible reason could be that he might feel abandoned. Growing up without them, he could resent the fact that they left him an orphan. He might think that if they were really so great, they would have found a way to survive and be there for him.
In some fanfictions, it might be due to an alternate reality. For example, if there was a different prophecy or a different turn of events at the time Voldemort attacked. Harry could leave his parents to fulfill a new - found destiny in this altered world. Also, it could be because of a miscommunication. A magical misunderstanding might lead Harry to believe he has to leave his parents for their own safety.
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.