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.
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 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 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 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.
It could also be that Naruto has had some sort of revelation about himself or the ninja world. He might have realized that the relationships he has been in were holding him back in some way. Maybe he wants to focus on self - improvement and growth, and he believes that being alone is the best way to do that. He could be trying to find his true self without the influence of others.
It could be due to a misunderstanding. Kakashi might think that Naruto is getting involved with something dangerous or has some potential that he can't handle. So, in his warped way of thinking, he abandons Naruto to protect him from himself or from some unknown danger.
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 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.