Perhaps there is a threat that Kakashi has detected, and he believes the best way to keep Naruto safe is to take him out of the village. It could be a group or an individual who is specifically targeting Naruto within the village, and by leaving, they can avoid this danger and also work on finding a solution to deal with the threat on their own terms.
It could also be that Kakashi wants Naruto to gain a broader perspective. In the village, Naruto is mostly surrounded by the same people and the same ideas. By taking him out, he can expose Naruto to different cultures, ninja techniques from other regions, and different ways of thinking. This will not only make Naruto a better ninja but also a more well - rounded person.
Maybe they come across a hidden, magical forest filled with strange creatures. Naruto's curiosity would lead them to explore deeper, and they would have to fight off some dangerous beasts. Along the way, Naruto could also discover new chakra - related secrets within the forest.
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.
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 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.
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.
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.