In some fanfictions, Harry could become withdrawn and depressed at first. Losing his place in Gryffindor is like losing his family. But then, he might find new strength and purpose, perhaps by joining forces with some outcasts in the wizarding world and forming a new group that challenges the unjust actions of Gryffindor house.
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.
Maybe Harry Potter is wrongly accused of a great crime in the wizarding world of England. The Ministry of Magic, fearing his power or influenced by dark forces in disguise, decides to banish him. He then has to start a new life in other parts of the magical world, perhaps in France or America, facing new challenges and making new friends along the way.
It could be Ares. He is often portrayed as a violent and unpredictable god. Percy might banish him if he goes too far in causing wars and chaos among mortals. His banishment would have a huge impact on the battlefields of the mortal world.
He'd probably be devastated at first. Gryffindor has been his home at Hogwarts, and his friends are there. But he's also a resilient character. He might start to question the fairness of the banishment and try to prove his innocence. He could look for allies outside of Gryffindor, like Luna from Ravenclaw, who might believe in him.
The main antagonist could be a power - hungry wizard in the Ministry of Magic. He might see Harry Potter as a threat to his rise to absolute power. So, he manipulates situations and spreads false rumors to get Harry banished.
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.
Fanfiction about Twilight Sparkle being banished can also be a vehicle for exploring different relationships. Maybe she meets characters she would never have interacted with in the show. Her banishment could bring out different sides of her personality. She might become more resourceful or develop a stronger sense of self - reliance as she tries to navigate her new situation.