One reason could be jealousy. If Naruto is getting more attention or has achieved more in the ninja world, his sister might be jealous and this could lead to her actions that hurt Naruto, either by spreading false rumors or directly confronting him in a hurtful way.
It might be due to an outside influence. Some dark force in the fanfiction could be using the sister as a tool. They might be implanting false memories or emotions in her, making her turn against Naruto and cause him pain without her fully realizing what she's doing.
It could be that his sister has some special abilities or talents that the family or the village values more. For example, if she has a very rare and powerful bloodline limit, everyone's attention would be drawn to her. In a ninja world, power and potential are highly regarded, so Naruto might be overlooked because his sister seems to have more of that 'special something' at first glance.
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.
It could be due to Sakura's feelings for Sasuke. If she's overly focused on Sasuke and Naruto gets in the way of her plans regarding Sasuke in some way, she might lash out and hurt Naruto without really meaning to cause serious harm.
If such a fanfiction exists, one possible reason could be a mind - control situation. Maybe an enemy uses some powerful genjutsu to make Naruto believe his sister is a threat, causing him to kill her accidentally. Another reason could be a misinformation plot where Naruto is tricked into thinking his sister has committed some unforgivable crime against the village.
One possible reason could be jealousy. Maybe his sister is jealous of Percy's special abilities or the attention he gets. Another reason might be that she is forced to abandon him due to some external threat or danger that she believes will harm her if she stays with Percy. Or perhaps she has been brainwashed into thinking that Percy is a bad influence or a danger to her.
One reason is that some fanfiction authors may lack a deep understanding of Naruto's character. They might write things that are completely contrary to his values and personality just for the sake of creating a 'unique' story. For example, Naruto is known for his positive attitude and strong will, but in some fanfictions, he could be depicted as a negative or spineless character.
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.
Maybe she's jealous of Naruto's popularity or his strength. It's possible that she feels overshadowed by him all the time and that jealousy turns into resentment, leading her to hurt Naruto.
Maybe there was some kind of powerful jutsu or curse involved. It could be that an enemy cast a spell on Naruto's family, making them forget about him.
One common reason is miscommunication. If Sakura misunderstands Naruto's intentions, she might react harshly and physically harm him. For instance, if Naruto tries to keep a secret from her to protect her, but she misinterprets it as betrayal.