Kakashi could be in a difficult situation where he has to make a choice between Naruto and another more pressing obligation. For example, he might be under orders from higher - ups in the village to focus on training a different group of ninjas. So, even though he may like Naruto, he has to reject him in order to fulfill his other duties.
In some fanfictions, Naruto might reject Sasuke because of Sasuke's continuous pursuit of power in a way that endangers others. Naruto, who values friendship and the safety of the village, could see this as a betrayal of their shared values.
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 reason could be that he sees Naruto as a younger version of himself in some ways. Both have had their share of loneliness and challenges growing up. Kakashi may want to prevent Naruto from going through the same pain he did. Another reason is Naruto's importance to the village. As the jinchuriki of the Nine - Tails, Naruto is a key asset. Kakashi, being a loyal ninja, wants to protect the village's future which is tied to Naruto.
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 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 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.
One possible reason could be training. Maybe Kakashi's training methods are too harsh for Naruto. Naruto is eager to become stronger quickly, but Kakashi might be holding him back in Naruto's eyes. For example, Kakashi could be making Naruto do repetitive basic drills instead of teaching him more advanced jutsu right away.
One reason could be that the fanfiction changes Kakashi's teaching methods too much. Naruto is used to Kakashi's unique style in the original story, and if it's drastically altered in a way that doesn't seem right to Naruto, he might not like it.
One reason could be Kakashi's Sharingan. It's a very powerful and somewhat spooky ability. Naruto might see it in action in a way that scares him. Maybe Kakashi uses it to subdue an enemy in a really intense way that makes Naruto realize how dangerous Kakashi can be.
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.