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.
One possible reason could be some sort of dark force influencing Kushina's mind. Maybe she was under a powerful genjutsu that made her think she had to abandon Naruto for his own safety, even though it was a false perception.
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.
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.
Sometimes, the source material itself can be a factor. If there are major changes in the official My Hero Academia storyline related to Izuku, it might make the author's original concept for the fanfiction no longer viable. Or perhaps they had planned the fanfiction to be part of a certain arc in the series, and when that arc didn't play out as they expected in the official story, they abandoned their work.
One reason could be that the author lost interest in the story or the character. Maybe they started another project that they found more exciting.
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.
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.
One possible reason could be a mission gone wrong. Maybe Kakashi thought Naruto was too much of a liability during a particularly dangerous mission and, out of a sense of harsh pragmatism, decided to abandon him to ensure the success of the mission and the safety of others. However, this would be very out of character for Kakashi as he has always been protective of his students.
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.
In some fanfictions, it could be due to his parents being on a dangerous mission. They might have been forced to leave Naruto in order to protect him from the enemies who were after them. Maybe they thought that by abandoning him, the enemies wouldn't be able to find him as easily. Another reason could be that they were under some sort of dark magic or curse that made them act against their will. This could lead to them leaving Naruto without any choice.