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.
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.
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.
One possible reason could be a misunderstanding. Maybe Naruto was misidentified as a threat in a tense situation. For example, if there was some sort of dark jutsu at play that clouded Kurenai's judgment and made Naruto seem like an enemy. Another reason might be that Kurenai was under some sort of mind - control. There are many villains in the Naruto universe who are capable of such things. If she was being controlled, she might unknowingly attack Naruto.
One possible reason could be his high - pressure job as Hokage. He might be so preoccupied with village affairs that he doesn't notice how his actions or words are affecting Fem Naruto. For example, he might cancel a promised training session with her because of an emergency meeting.
Maybe she's been possessed. In some fanfictions, characters can be taken over by dark forces. So Kushina could be under the control of some evil entity and that's why she hurts Naruto.
One possible reason could be a misunderstanding. Maybe Tsunade received some false information about Naruto that made her think he was a threat to the village, so she took actions that ended up hurting him.
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 reason is that batjokes may not fit the mood of the fanfiction. Fanfiction often has its own atmosphere and theme. If batjokes are too comical or out of place in a more serious - themed fanfiction, it can ruin the overall feeling. For example, in a dark and gritty Batman - related fanfiction, a silly batjoke can break the immersion.
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.
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.