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.
Perhaps there's a misunderstanding within Gryffindor. A prophecy is misinterpreted to suggest that Harry will bring doom to the house. So, they exile him. As a result, Harry has to find new allies among the other houses or even among the outcasts of Hogwarts. He might discover new magical abilities or secrets in his quest to clear his name and get back to Gryffindor.
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.
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.
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 a 'Harry Potter betrayed by Gryffindor' fanfiction, perhaps there is a prophecy that is misinterpreted. The Gryffindors think Harry is the cause of upcoming doom instead of the savior. So, they begin to betray him. Harry would then have to struggle not only with the external dark forces but also with the internal pain of being rejected by those he considered friends and housemates. He might start to question his own identity and values, and his journey would be about regaining the trust of Gryffindor or finding his own path without them.
Well, it could be that there's a misunderstanding. Maybe some Gryffindor students think Harry has done something wrong, like he's been framed for a crime in Hogwarts. So they turn against him in anger and attack him. But later they find out the truth and feel really guilty.
Well, it could be about Harry struggling to fit in with the typically bold Gryffindors. Maybe he has a hard time speaking up in class or during Quidditch matches. He might have a small group of close friends who help him come out of his shell.
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.