Well, considering Hinata's character, we know she is very traditional. She might view fanfiction as something that distorts the true story and values of the Naruto world. There is no one incident but her overall personality traits suggest she would be averse to it. For instance, she has always been respectful of the ninja code and the way things are in the village, and fanfiction can be seen as going against that order in a way.
Maybe she wants to keep her real relationship with Naruto pure. Fanfiction can be full of all sorts of wild and untrue interpretations of their relationship. She values what she has with Naruto in reality and doesn't want to be influenced by fictional ideas. For example, some fanfictions might create unnecessary drama or unrealistic scenarios between them.
One reason could be to explore new storylines and relationships outside of the traditional Team 7 dynamic. In fanfiction, authors often like to break away from the norm. Maybe Naruto wants to develop his own skills independently without relying on his team. Another possibility is that there could be some sort of conflict or misunderstanding within the team that makes him want to avoid them in these fictional stories.
Another reason could be in a fan - created scenario where there are secrets involved. Hinata might be keeping a secret from Naruto that, when revealed, makes Naruto feel betrayed or deceived. This sense of betrayal could easily turn into anger. For instance, if Hinata has a connection to an enemy that she's been hiding from Naruto.
Maybe in the fanfiction, Naruto has made some decisions that go against Hinata's beliefs or values. Suppose Naruto decides to use a very dangerous and unethical jutsu for power, and Hinata, who is usually very moral, might start to hate him for that.
Some writers might write a 'Naruto Rejects Hinata' fanfic to introduce more drama or conflict into the story. By changing the canon relationship, they can create new story arcs and plot twists. For example, it could lead to Hinata developing in a completely different way or even becoming a rival to Naruto. Additionally, it could be a way for the author to express their own creativity and not be bound by the original storyline.
However, Naruto is also a very loyal and understanding person deep down. So after the initial shock and anger, he would probably start to investigate the situation more. He might talk to their friends like Shikamaru or Sakura to see if they know anything. He would want to get to the bottom of it rather than just making a hasty judgment.
One possible reason could be for the sake of creating a more complex love triangle in fanfiction. Maybe the writer wants to explore a different dynamic where Naruto and Hinata's relationship is strengthened by having a common dislike for Sakura. It could also be that the fanfiction writer is trying to give Hinata more agency and make her a stronger character by having her oppose Sakura in some way, perhaps in matters related to Naruto's affections.
The weather could pose a challenge. If they go to a place with unpredictable weather, like a mountain area, they might get caught in a storm. Naruto would try to protect Hinata from the elements, but they could end up lost or having to find shelter in a less - than - ideal place. Also, adjusting to living together in such a close and new way could be difficult for both of them.
It could be someone new that the author creates just for the fanfiction, someone Naruto meets during a mission perhaps.
One common scene is when Naruto is frustrated after a failed mission. Hinata finds him alone, and she sits beside him in silence for a while. Then she starts to talk about how everyone makes mistakes and that it's a part of growing. This simple act of sharing her perspective calms Naruto down.