Perhaps he leaves Gryffindor in fanfiction because he is influenced by a new mentor or friend who is from a different house or group. This person might convince him that he can achieve more or be more true to himself outside of Gryffindor. Also, it could be due to a prophecy or a special mission that requires him to distance himself from Gryffindor for a while to protect the house or the entire Hogwarts from a certain threat.
He may leave Gryffindor if he becomes disillusioned with the house's values over time. Maybe he witnesses some actions or attitudes within Gryffindor that go against what he believes in. For instance, if Gryffindors start to show excessive pride and competitiveness in a negative way, and Harry, who values fairness and unity more, decides he can't be part of it anymore.
One possible reason could be a misunderstanding with his friends in Gryffindor. Maybe there was a big argument over something like a Quidditch match strategy that made him feel alienated.
One possible reason could be a fallout with his friends in Gryffindor. Maybe he feels betrayed by them in some way in the fanfiction world. For example, if they wrongly suspect him of something.
One possible reason could be a false accusation of using dark magic. In some fanfictions, the wizarding world can be very paranoid about dark magic, and if Harry was wrongly suspected of delving into it, Gryffindor might exile him to protect their reputation.
One reason could be that he doesn't like the spotlight that comes with being a Gryffindor. In the original story, Gryffindors are often in the limelight, and in fanfiction, he might be tired of all the attention.
Maybe he's falsely accused of stealing important Gryffindor artifacts. For instance, if the Sword of Gryffindor goes missing and Harry is wrongly blamed, the house might decide to kick him out. It could be part of a plot by a jealous student or an outside force trying to disrupt Hogwarts.
In some fanfictions, it could be a political move within Hogwarts. There might be a group that wants to undermine Dumbledore's influence, and since Harry is so closely associated with him, they target Harry by getting him banished from Gryffindor. This could also be related to the discovery of some long - hidden secret about Harry's family that makes the Gryffindors view him differently.
Another reason could be related to a new prophecy. Suppose a new prophecy emerged that said Harry Potter's presence in Gryffindor would bring great danger to the house. The Gryffindor students and faculty, believing in the importance of protecting the whole house, might have decided to banish him. But of course, this would be a very difficult decision as Harry has been an important part of Gryffindor before. And in the end, the prophecy might turn out to be misinterpreted.
One reason could be that the official Harry Potter canon is so extensive and detailed that it overshadows fanfiction. The original story has such a rich world, characters, and plotlines that it becomes the main focus for many fans, leaving less room for fan - created stories.
The dynamics within Gryffindor would be greatly affected. His friends like Ron and Hermione would be confused and sad. The Gryffindor house would lose one of its most iconic members, and there might be a power shift within the house. Other Gryffindors might feel less confident without Harry around.
One possible reason could be to protect them. In many fanfictions, Harry might believe that by distancing himself from his friends, he can keep them out of danger. For example, if there is a new dark threat targeting him specifically, he may think that the enemy will use his friends against him.