In some fanfictions, there could be an alternate reality where the power dynamics are completely different. Maybe Naruto has been possessed by an evil force and Kakashi, in an attempt to save the world from this greater evil, has to take the drastic step of killing Naruto. Or perhaps there is a prophecy that Naruto will bring about the end of the world, and Kakashi, being a protector of the village, believes he has no other choice but to stop Naruto, even if it means killing him. These are just some of the possible reasons that could be explored in a fanfiction.
One possible reason could be a misunderstanding. For example, if Naruto was thought to be a threat to the village in a way that Kakashi misinterpreted the situation. Another could be that in a fanfiction where there is a dark curse or power that corrupts Kakashi's mind and makes him see Naruto as an enemy. It could also be part of a complex plot where sacrificing Naruto was seen as the only way to save the greater good according to Kakashi's warped perception in that particular fan - written scenario.
Maybe in a fanfiction where Kakashi is mind - controlled. It could lead him to harm Naruto without his normal self - control.
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 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.
Well, it could be that Kakashi is under some sort of dark spell or curse that makes him see Naruto as a threat to the village. In some fanfictions, there might be a situation where the village's safety is at stake and Kakashi believes that sacrificing Naruto is the only way to save everyone. Also, it could be a case of false information. If someone convinces Kakashi that Naruto has turned evil and is about to cause great harm, he might take the drastic step.
One reason could be Sasuke's thirst for power. If he believes Naruto is the only obstacle in his path to ultimate power, he might be driven to kill him. In some fanfictions, Sasuke may be influenced by a dark entity that twists his mind into thinking Naruto is a threat that needs to be eliminated.
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.
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 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.
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.