Perhaps his sisters in the fanfiction are simply written as cruel characters for the sake of creating drama. However, in a more in - depth exploration, it could be due to a misunderstanding. They might think Naruto has done something wrong when in fact he hasn't. This misunderstanding then escalates into abuse as they fail to communicate properly with Naruto.
One possible reason could be jealousy. Maybe Naruto has some special abilities or is getting more attention in some way that makes his sisters envious. So, they take out their frustrations on him through abuse.
One possible reason could be to protect her. Maybe she has some special power that attracts dangerous enemies, and Naruto, being the strong and protective character he is, seals her power to keep her safe from those who might misuse it.
It could also be related to her popularity among their peers. If his sister is more well - liked and has a lot of friends, Naruto, who has often been an outcast, might feel envious. He might wish he had the same social skills or charm that his sister has, which allows her to fit in so easily.
The abuse from his sisters in fanfiction could have a profound impact on Naruto's character development. It could shatter his innocent view of family and relationships. He may struggle with feelings of anger and resentment. But as he grows, he could either let these negative feelings consume him or use them as fuel to break free from the cycle of abuse and become a better person, perhaps even finding a way to forgive his sisters if he discovers the root causes of their actions.
One possible reason could be to protect her. Naruto might believe that by leaving, he can draw danger away from his sister. For example, if there are powerful enemies targeting him, he doesn't want his sister to get caught in the crossfire.
I'm not sure if there is such a specific fanfic. Fanfics cover a wide range of themes, but abuse within family in a Naruto fanfic might be a rather dark and not - so - common take. It could exist in some corners of the vast fanfic community, but it would also be quite controversial as Naruto is generally depicted in positive relationships in the original series.
Another possibility is that they leave because of a sense of disillusionment. They could have witnessed some corruption or unfairness within Konoha's leadership or among the ninja community. This makes them lose faith in the village and decide to start anew elsewhere.
One possible reason could be fear. Naruto has the Nine - Tailed Fox sealed within him. His clan might have been afraid that this power could bring destruction upon them, so they chose to abandon him. Another reason could be a misunderstanding. Maybe they thought Naruto was somehow in league with the forces that brought the Nine - Tailed Fox to the village in the first place.
Maybe in the fanfic, his sisters got some special powers or attention that Naruto felt was unfair. So he started to hate them out of envy.
One possible reason could be a sense of betrayal. Maybe he discovers some long - hidden secrets about his family that make him feel they are not who he thought they were. For example, if he found out his parents had some kind of deal with the village elders that he disagreed with.
It could be that there was a prophecy related to his sister that made the family think she was more important. For example, a prophecy that she would be the key to saving the village in the future. And in their short - sighted view, they abandoned Naruto to focus all their resources on her.