Maybe in some fanfictions, the writer portrays Kakashi in a way that Naruto doesn't resonate with. For example, if Kakashi is written to be too strict or distant in a different way than in the original story, Naruto might not like that version of him.
One possible reason could be miscommunication. Maybe Kakashi has been involved in some secret missions or decisions that Naruto doesn't understand, leading to a breakdown in trust. For example, if Kakashi made a call during a battle that put Naruto or his friends in danger without fully explaining it to Naruto later.
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.
Maybe Naruto just sees Sakura as a friend. He might have a different idea of his ideal partner and Sakura doesn't fit that. His feelings for her could be purely platonic.
One possible reason could be his past traumas. Naruto grew up alone and was often shunned by the villagers. Physical touch might remind him of the times when he was pushed away or bullied, so he has developed an aversion to it in fanfiction.
Well, in some fanfictions, it might be because the writer wants to create an alternative storyline. Maybe they think Naruto has a different type of relationship in mind, like a more platonic or brother - sister - like bond with Hinata instead of a romantic one.
The story could introduce a new character as Naruto's mentor. This character might have a completely different teaching style compared to Kakashi. Maybe this new mentor focuses more on spiritual growth rather than physical combat skills. As a result, Naruto would develop in a new and unexpected direction, which would make the fanfiction more interesting. For instance, Naruto could learn more about the history and philosophy of the ninja world, which would give him a deeper understanding of his role as a ninja.
Yes, in some fanfictions, Naruto can be like Kakashi. Writers might give Naruto some of Kakashi's traits, like his calmness in battle or his love for reading. This can make for an interesting twist in the story.
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 this kind of fanfiction, Naruto might be dressing like Kakashi for various reasons. Maybe it's part of a mission where he has to go undercover. He could be trying to imitate Kakashi's cool and mysterious aura to deceive the enemy.