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.
It might be that he has different values than what Gryffindor represents in the fanfiction. For example, if the fanfiction portrays Gryffindor as being too quick to judge based on the sorting hat's decision, Harry might oppose that. He could think that people should be judged by their actions rather than a hat's choice.
One reason could be that the fanfic distorts the characters he knows well from Gryffindor. For instance, if it changes the personalities of his friends in Gryffindor in a way that doesn't seem right to him.
One reason could be a personal betrayal. Maybe a close friend from Gryffindor betrays Harry, and this makes him start to dislike the whole house. It's like when one bad apple spoils the bunch in his eyes.
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.
Well, it could be that the fanfiction writer is trying to subvert the traditional narrative. Harry has always been the hero of Gryffindor, but in this new take, he hates it. Maybe he sees the flaws in Gryffindor that are often overlooked in the original story, like the over - emphasis on courage which can sometimes lead to recklessness and he doesn't like being part of a house with such a one - dimensional view of what's important.
She might hate it because it could change the way people see her character. In the original story, she is a strong and independent person, but fanfiction might portray her in a wrong way.
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.
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.
It could also be that the fanfic might interfere with the way he wants his story to be remembered. His adventures at Hogwarts were real and important to him, and when fanfic changes the narrative, it's like his story is being disrespected. For example, if a fanfic portrays him as cowardly when he was actually brave, that would surely make him dislike it.