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.
Well, in certain fanfiction scenarios, Harry could be lured away from his parents by a powerful magical being who has some sort of ulterior motive. This being could convince Harry that leaving his parents is the only way to save the wizarding world. Or perhaps, in a really complex fanfiction plot, Harry discovers a hidden truth about his family that makes him feel like he has to distance himself from his parents in order to protect them or the wizarding world at large.
Another reason could be a misunderstanding. Maybe he overhears something Harry and Hermione say and misinterprets it as them not wanting him around anymore. So, in a fit of anger and hurt, he leaves. This can lead to a lot of angst and drama in the fanfiction as the other characters then have to figure out how to get him back.
Perhaps he leaves in search of a more peaceful life. The wizarding world, despite its magic, has been filled with turmoil for him. He could be seeking a place where he can simply be Harry, not 'The Boy Who Lived' or the hero who defeated Voldemort. He may also be on a quest to discover more about his family's past in the Muggle world, something that has been somewhat overlooked in his life in the wizarding world.
In the fanfiction world, it could be a prophecy. There might be a prophecy that says Harry's presence in Ginny's life will bring great harm to her or the wizarding world. So, for the greater good, Harry leaves. He believes that by sacrificing his relationship with Ginny, he can save her and everyone else. It's a very noble but also a very heart - breaking decision.
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.
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 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 in the fanfiction, Harry might have discovered some dark secrets about his parents that made him feel betrayed. For example, if he found out they had some hidden and unethical magical experiments in their past.
One reason could be a falling - out with his friends in Gryffindor. Maybe there was a misunderstanding that grew so large that he felt he couldn't stay. Another possibility is that he might be lured away by some mysterious force or character who convinces him that Gryffindor is no longer the right place for him. For example, if a new group claims to have a better way to fight Voldemort and they are from a different 'house' in this fanfiction concept.
One possible reason could be that Harry discovers some secrets about Dumbledore that make him lose trust. For example, if he finds out about Dumbledore's past mistakes or hidden agendas that he doesn't agree with. Another reason might be that Harry feels he can better protect his friends and fight Voldemort on his own terms, away from Dumbledore's influence and strategies which he may start to question.
One possible reason could be to escape the fame and the constant scrutiny that comes with being 'The Boy Who Lived'. After all the battles and chaos, he might just want some peace and quiet to heal his mental and emotional wounds.