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.
In some fanfictions, Kakashi could be written to be too cold towards Naruto. In the original series, there is a bond between them, but if the fanfiction breaks that bond by making Kakashi unfeeling towards Naruto, Naruto would not like that portrayal of Kakashi.
It might be that the fanfiction gives Kakashi a different set of values that conflict with Naruto's. Naruto values things like loyalty, hard work, and friendship, and if Kakashi in the fanfiction goes against these values, Naruto would not like him. For example, if Kakashi is shown to be disloyal to the village in the fanfic, Naruto would surely dislike that version of him.