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 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.
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 that Kakashi is preoccupied with other important matters in the village. Maybe he has some top - secret missions or tasks assigned by the Hokage that demand his full attention, leaving him with little time to focus on Naruto.
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 the fanfiction alters the relationship between Kakashi and Naruto in a way that Kakashi doesn't like. Maybe it shows Kakashi as being overly harsh or unfair to Naruto in a situation where in the original series he wouldn't be. It could also be that the fanfiction contains plot elements that Kakashi, as a character, would find illogical or against the spirit of the Naruto world.
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 reason could be that some fans are very purist about the original Naruto story. They might feel that fanfiction often distorts the characters or the plot in ways that go against the essence of what Naruto is all about. For example, changing a character's personality completely to fit a romantic or dark and edgy narrative that doesn't align with the source material.