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 possible plot could be that Harry is framed for something he didn't do. Maybe a powerful dark object is found in his dorm, and the Gryffindor house, fearing for their reputation and safety, decides to exile him. Harry then has to prove his innocence while also dealing with the isolation and new challenges outside of his familiar house.
A dark force that has the ability to influence the minds of Gryffindor members. This could be a powerful and ancient magic or a new form of dark magic. It turns the house against Harry without them fully realizing it, making the collective Gryffindor house, under this influence, seem like the antagonist.
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.
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.
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.
He would probably be extremely hurt. Gryffindor was like his family at Hogwarts, so being exiled would be a huge blow. He might initially feel angry and betrayed.
In some fanfictions, it could be due to a misunderstanding. Maybe someone framed Harry for a serious rule violation that Gryffindor's house values highly, like cheating in an important magical exam. And the evidence against him seems so strong that the Gryffindor house decides to banish him.
In some fanfictions, the author might create a situation where Harry's actions lead to great harm to Gryffindor as a whole. For instance, if he makes a decision that causes Gryffindor to lose a significant amount of points in a crucial time, like right before a major competition. This could lead to his censure as the house would see him as a liability. Also, if he gets into a feud with important Gryffindor figures, like the prefects or the head of the house, it could result in his censure.
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.