One possible reason could be a misunderstanding. Maybe Sakura did something that Naruto misinterpreted as a betrayal or lack of support. For example, if she sided with someone against Naruto in a village decision without fully understanding the situation.
It could also be due to Naruto's own insecurities. He might have thought that Sakura didn't truly see him as a friend or an equal. Perhaps he overheard Sakura saying something negative about him to someone else, which made him lash out with 'I hate you'.
Another reason could be related to a plot by an enemy. An antagonist might have used some form of mind - control or false information to make Naruto believe that Sakura was a threat. So in his confused state, he said he hated her.
Sakura might then get angry. Instead of being sad right away, her pride could make her retaliate. She might say something like 'Fine, if you hate me, then stay away!' but deep down she would be hurt.
Maybe Naruto hates it because the two universes have very different power systems and cultures. Naruto's world is about ninjas, chakra, and village politics, while Avatar has bending elements and a different kind of spiritual connection. The fanfiction might misinterpret or blend these in a way that doesn't sit well with Naruto fans who are purists.
One possible reason could be that she might have underestimated Naruto in the past. She often belittled his abilities and dreams, but as she grew and realized his true strength and determination, she felt the need to apologize for her previous behavior.
One reason could be the way Hiruzen treated Naruto as a child. In the original, Naruto was kind of an outcast, and if in fanfiction, Naruto blames Hiruzen for not doing more to prevent that, he could hate him. Another reason might be related to Hiruzen's decisions regarding the Uchiha clan. If Naruto in fanfiction feels that Hiruzen's actions led to bad consequences for the village and his friends, he might develop hatred.
Perhaps in the fanfiction, Dark Naruto has been betrayed. It could be that someone he trusted deeply, like a mentor or a close friend, turned on him. This act of betrayal could make him lose faith in humanity and lead to his hatred for everyone. He might think that if one person can betray him, then anyone can, so he hates them all without distinction.
One reason might be that he doesn't like how fanfiction can change the relationships between characters. For example, in the original, his relationship with Naruto is based on training and mentorship, but fanfiction could make it something completely different.
One possible reason could be a misunderstanding. Maybe some false information was spread about his mother, making Naruto believe she had abandoned him. Another reason could be related to the secrecy around his mother. If he grew up feeling alone and not knowing about her, he might develop resentment.
Perhaps Sakura is in a state of extreme stress. Maybe she has a lot of pressure on her, like trying to save a village or a loved one, and Naruto's actions, which might seem reckless to her at the time, cause her to snap and hurt him without really meaning to.
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 reason could be Naruto's recklessness. In fanfiction, Naruto might do something extremely dangerous without thinking, and Sakura, being worried about his safety, yells at him. For example, if he decides to take on a powerful enemy alone without a proper plan.