Perhaps Naruto blames Kakashi for not being able to prevent some bad things from happening. For example, if a friend of Naruto gets hurt during a mission that Kakashi led, Naruto could hold it against him. Kakashi, as the leader, might seem responsible in Naruto's eyes.
It could also be that Naruto has different ideals from Kakashi. Naruto is very straightforward and eager to prove himself, while Kakashi has his own more reserved and complex way of doing things. This difference in approach might lead to Naruto feeling that Kakashi doesn't understand him and thus hating him.
One possible reason could be that Naruto might feel Kakashi is too strict with his training. Maybe Kakashi's methods are too harsh for Naruto, making him frustrated and gradually developing dislike.
One possible reason could be that in the fanfiction, Kakashi might have made a decision during a mission that Naruto strongly disagreed with. For example, Kakashi could have chosen to sacrifice something important to Naruto in order to achieve the overall mission objective.
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.
Perhaps he thinks fanfic undermines the integrity of the original Naruto story. The official story has a certain narrative and character development, and fanfic can deviate from that significantly. When it comes to his connection with Naruto, any deviation in fanfic might be seen as a negative. For example, if a fanfic changes the way he mentors Naruto, it could be something he wouldn't like.
One possible reason could be Kakashi's reputation as a strict and powerful teacher. Naruto might be in awe of his skills and fear making mistakes in front of him.
One possible reason could be that Naruto might be trying to prove his independence. He has grown and wants to show that he can handle things on his own without always relying on Kakashi's guidance.
Perhaps in this fanfiction's universe, Naruto's goals and ideals are completely different from Kakashi and Sakura's. Naruto may be aiming for a more radical change in the ninja world, while Kakashi and Sakura are more conservative. Their differences could lead to Naruto developing a sense of hatred towards them as they constantly oppose his ideas.
Perhaps Kakashi feels that Naruto is becoming too reliant on him and not developing his own skills independently. So, in order to force Naruto to become stronger on his own, he decides to abandon him. This is a tough - love approach. Naruto has great potential, but he needs to learn to stand on his own two feet, and Kakashi may think this is the best way to make that happen.
In the fanfiction, it could be that Kakashi is being too hard on Naruto during training. He might be pushing him beyond his limits without proper explanation or support, causing Naruto to feel frustrated and angry. Naruto is a determined character, but everyone has their breaking point.
One possible reason could be that Kakashi might be haunted by his past experiences. He has lost many comrades, and perhaps he's afraid that getting too close to Naruto and training him would put Naruto in danger as well. He might think that Naruto, being the Jinchuriki of the Nine - Tails, already has a target on his back, and training him would only make that target bigger.
Maybe Naruto admires Kakashi's skills. Kakashi is a highly respected ninja, and Naruto might want to be as good as him. So he starts acting like him to learn from him.