Another reason could be that fanfiction has the potential to create alternate universes that deviate too much from the canon. Naruto fans who are very attached to the official story might fear that these extreme deviations in fanfiction could overshadow or misinterpret the original narrative. For instance, a fanfiction that makes Naruto into a villain instead of a hero might be feared by those who cherish the original story.
In some fanfictions, Naruto might be feared due to his overwhelming power. For example, if he has some new and extremely dangerous jutsu that others can't understand or counter. It could also be because he has changed his personality to be more cold - blooded and less forgiving, which is a departure from his original kind - hearted self in the official story.
Naruto might dislike fanfiction because it can be a source of misinformation. Fans who read fanfiction might get the wrong idea about him or his world. He wants people to understand his story as it was originally intended. The original Naruto story is a carefully crafted narrative about ninja life, dreams, and the pursuit of peace. Fanfiction can deviate from this and make it seem like something else entirely, which he would find unacceptable.
One possible reason could be that Hiashi might see Naruto as a threat to the Hyuga clan's secrets or traditions. Naruto is often associated with unpredictable and powerful abilities, and Hiashi, being protective of his clan, may want to keep him at a distance to safeguard the clan's interests.
One possible reason could be that the fanfiction misrepresents the Uzumaki clan or Naruto's connection to it. Naruto has a deep and complex relationship with his Uzumaki heritage, and if the fanfiction distorts it, he might dislike it.
It could also be due to the overall tone and plot of the fanfiction. If the fanfiction has a dark or negative theme and Yasaka is a part of that in a way that makes Naruto seem to 'hate' her, it might be because the writer wants to create some sort of conflict. However, this may not align with the original essence of Naruto's character, who usually tries to understand and befriend rather than hate without a good reason.
Maybe Naruto, as a character with his own set of values and storylines in the original Naruto universe, clashes with the concepts often presented in Olympus - related fanfiction. For example, the Naruto world has its own unique power systems, cultures and ethics which might be very different from what is typically found in stories related to Olympus.
He could leave because of a broken heart over a lost love. If Naruto had strong feelings for someone in Konoha, like Sakura, and she chose someone else or rejected him in a cruel way, it might be too much for him to bear. So he decides to leave the place full of memories related to that person.
Well, it could be that the fanfiction distorts the original Naruto story in ways that are unappealing. Maybe it goes against the core values or the character development in the Naruto universe.
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.
One possible reason could be that Kakashi later realizes Naruto's potential. He might see how much Naruto has grown on his own despite being ditched, and feels guilty for not being there to guide him more. Another reason could be that Kakashi starts to understand the importance of Naruto in the overall story or the team's dynamic. Maybe he misses the bond they could have had if he hadn't ditched Naruto.