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.
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.
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.
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.
Well, Kakashi could train Naruto in combat skills specific to ANBU missions. This would include more lethal and precise attacks. He might also teach Naruto how to use different types of weapons that are common in ANBU operations. Maybe Kakashi would set up mock battles where Naruto has to face multiple opponents at once, just like in real ANBU scenarios.
In some fanfictions, Kakashi might train Naruto by creating extremely challenging survival scenarios. For example, he could drop Naruto in a mock battlefield filled with various traps and enemies that Naruto has to overcome using his skills and wits. This forces Naruto to think on his feet and improve his combat abilities quickly.
Another option could be Itachi. Although Itachi is from a different village and has his own complex situation, in a fanfiction scenario, he could secretly train Naruto. Itachi has extremely powerful jutsus and a deep understanding of the Sharingan. Training under him would give Naruto a very different perspective on power and combat, not to mention some insights into the Uchiha clan.
Naruto might be initially very disappointed. He has always looked up to Kakashi as a strong and cool ninja, and being refused by him would be a big blow. He could become a bit sulky and withdrawn, feeling like he's not good enough.
Naruto might develop different skills. Without Jiraiya's training, he could focus more on self - taught techniques or learn from other characters. For example, he might learn more about the Uzumaki clan's unique abilities from someone else in the village.
Well, in the original story, Jiraiya played a big role in Naruto's emotional growth too. If he doesn't train Naruto in the fanfiction, Naruto might lack the father - figure like guidance that Jiraiya provided. This could lead to Naruto making different decisions in life, both in terms of his relationships and his ninja career. For example, he might not have the same understanding of the ninja world's politics and power struggles, which could put him at a disadvantage. Also, his connection to the Sage Mode might be completely different or non - existent, which would change how he fares in battles against powerful enemies.