It could also be because of Naruto's own insecurities. He might be afraid that Hinata's actions are drawing too much unwanted attention or putting herself in harm's way, and he yells to try and protect her in his own, brash way. He doesn't want to lose her, but doesn't know how to express it other than through yelling.
Perhaps there is some external pressure on Naruto, like from the village elders or other powerful ninjas. They might be pressuring Naruto to keep Hinata in line, and he yells at her as a result. He doesn't really want to, but feels he has no choice in order to satisfy those in power.
Hinata might be very hurt. She's a sensitive person, so Naruto yelling at her could make her feel small and sad. She might start to doubt herself and her abilities.
One possible reason could be Snape's unfair treatment of Gryffindor students. Hermione, being a strong advocate for justice, might not tolerate his constant bias against her house. She could yell at him when he unjustly deducts points from Gryffindor for minor reasons.
One possible reason could be that Harry did something reckless without consulting Hermione. For example, if he went off on his own to face a dark wizard, Hermione, being the cautious and logical one, would be furious. She values planning and teamwork, and Harry's solo actions might seem to her as endangering himself and others needlessly.
One possible reason could be Sakura's constant pining for Sasuke. Naruto might feel frustrated that she's so focused on Sasuke when he's right there for her. In the Naruto universe, Naruto has always been a bit jealous of Sakura's love for Sasuke, and in fanfiction, this could be amplified to the point where he yells at her out of pent - up emotions.
One possible reason could be a misunderstanding. Maybe Naruto misinterprets Hinata's actions or words and distances himself from her. For example, if Hinata is trying to be helpful in a certain situation but Naruto takes it the wrong way. Another reason might be external influence. If there are other characters who try to drive a wedge between them, like some jealous rivals who spread false rumors about Hinata to Naruto. Also, Naruto's own insecurities could play a part. He might feel that he's not good enough for Hinata and decides to let her go on his own accord.
Perhaps in the fanfic, Hinata has fallen in love with someone else. It could be a new character introduced in the fanfic's universe or someone she has come to know better over time, leading her to reject Naruto.
It could also be due to jealousy. If Naruto is spending a lot of time with other female characters, Hinata might get angry. Even though she is usually shy and reserved, her love for Naruto could turn into anger if she feels threatened by his closeness to others.
One reason could be for the sake of creating drama. Writers might want to explore how the Naruto universe would be shaken up by such an event. It could also be a way to explore different character aspects of Naruto and Hinata that aren't shown in the original, like how Naruto would react to such betrayal.
One possible reason could be that in the fanfic, Hinata has different personal goals or ambitions that she feels would be compromised if she were to be with Naruto. For example, she might be more focused on her family duties or her own ninja training and career, and she believes that a relationship with Naruto would distract her from those things.
Well, one reason could be that some fans are just exploring alternative storylines out of boredom. They might think it's interesting to see what would happen if they break the established relationships in the Naruto world. Another reason could be that they are trying to add more drama to the story. However, these fanfics don't represent the true nature of the Naruto characters as they are in the official series.