Maybe he's trying to hide his identity for a secret mission. In some fanfictions, Naruto might be undercover, and covering his face is a simple way to avoid being recognized.
The Joker cutting his face off is a symbolic act of completely letting go of any pretense of normalcy and embracing his insanity to the fullest. It's a shock tactic to terrorize and confuse his enemies.
Perhaps he's trying to protect himself from some kind of danger. There could be an enemy who is looking for him and by covering his face, he can avoid being detected easily. It could also be a part of a new jutsu or power he has discovered where covering his face is necessary for its activation or control.
Well, it could be that Kakashi, being a character who values the integrity of the original Naruto narrative, sees fanfiction as a deviation. Fanfiction might include out - of - character scenarios for him or the other characters. He might also dislike the fact that some fanfictions can be of very poor quality in terms of writing and plot, which could be a reason for his dislike.
Maybe he thinks fanfic often distorts the real story or characters of Naruto. In the original Naruto series, Kakashi has his own understanding and relationship with Naruto. Fanfic might create some scenarios that go against his view of Naruto or the world they live in.
In this fanfiction, Kakashi could help Naruto in his training through mental conditioning as well. Naruto is often impulsive, so Kakashi may work on his patience and decision - making skills. He could use his Sharingan (if applicable in the fanfiction) to analyze Naruto's movements during training and give him detailed feedback. Moreover, Kakashi could introduce Naruto to different types of enemies and battle scenarios in a controlled training environment, which would broaden Naruto's understanding of combat and make him a more versatile ninja.
In the fanfiction, Kakashi might face the challenge of Naruto's insecurities. Naruto has always had a complex about being alone and not having a family. Kakashi would have to find ways to make Naruto feel secure and loved. Also, dealing with Naruto's powerful and sometimes uncontrollable chakra could be a problem. Kakashi would need to train Naruto to master his chakra properly without it overwhelming him.