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.
In the fanfiction, Naruto could act like Kakashi because he wants to understand him better. They are comrades, but Kakashi has a lot of hidden depths. By acting like him, Naruto hopes to get into his mindset. Also, Naruto may believe that acting like Kakashi will help him gain more respect from the other ninjas. Kakashi is well - respected in the ninja world, and Naruto might think that by imitating his behavior, he will be taken more seriously.
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 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 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.
Another reason could be that in this fanfiction, the plot is set in a way that there is a new training system in the village. And this system doesn't involve Kakashi in Naruto's training. There could be new mentors or a completely different approach to training young ninjas like Naruto, which excludes Kakashi from the equation.
Perhaps there was some sort of dark influence or mind - control at play. An enemy might have manipulated Kakashi's mind in such a way that he believed Naruto was a threat and thus left him for dead, not realizing his true self.
One possible reason could be that Kakashi might think Naruto is not ready yet. Maybe Naruto hasn't mastered some basic skills that are prerequisites for the more advanced training Kakashi has in mind. Another reason could be that Kakashi is worried about Naruto's recklessness. Naruto has a tendency to rush into things without thinking, and Kakashi might fear that this could lead to Naruto getting seriously injured during the training.