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.
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.
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 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.
In some fanfiction, Harry leaves to seek more powerful magic. He realizes that the magic in Britain is somewhat limited in the fight against Voldemort. So he travels to other places, like ancient magic - rich regions in Asia or Africa, to find a way to defeat Voldemort. He hopes that by leaving, he can gain the upper hand in the battle.
Maybe he's tired of the spotlight in England. In some fanfictions, he could be seeking a new start away from the prying eyes and the constant media attention that comes with being in England.
One possible reason could be a major disagreement with the Gryffindor house leadership or some of the students. Maybe he feels that they are not living up to the values he thought they held. Another reason might be that he discovers some dark secret within Gryffindor that makes him uncomfortable and he decides to leave.
Physically, he might become more rugged and less concerned with his appearance. Without the trappings of wizarding society, he may grow a beard or let his hair get long and unkempt. Mentally, he could become more introspective. He has time to think about all that has happened in his life, and this could lead to a deeper understanding of himself and the events that shaped him.
In some cases, he could be leaving in search of a greater purpose. He might feel that there are things he can learn or achieve outside the wizarding world that will ultimately help the wizarding community more. He may also leave because of some prophetic vision or a feeling that he doesn't belong there anymore, that his path lies elsewhere, away from the familiar magical realm he grew up in.
In some fanfictions, Harry might leave his family because of a prophecy or a special mission. He might feel that he has to go it alone in order to fulfill this prophecy or complete the mission successfully. His family might not understand or be able to support him in this, so he decides to leave. Also, there could be jealousy or resentment within the family that makes the environment unbearable for Harry.