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.
Perhaps Sasuke is possessed by some extremely evil entity. And Kakashi, in an attempt to stop the entity from causing more destruction, decides to kill Sasuke. It could also be that Sasuke discovers some dark secret about Kakashi that Kakashi doesn't want revealed, and in a moment of panic and self - preservation, he kills Sasuke.
One possible motive could be to help Naruto control the Nine - Tails' chakra better. Hypnosis might be a way to reach into Naruto's subconscious and find a way to coexist with the powerful force inside him.
One possible motive could be jealousy. If Kiba were to gain more recognition in the village than Naruto in the fanfiction world, Naruto's insecurities could drive him to do something drastic like killing Kiba. But this is a huge departure from his usual self.
One possible motive could be mind control. Maybe an enemy manages to take over Kakashi's mind and forces him to harm Naruto. Another could be a misunderstanding. For example, if Naruto was thought to be possessed by a powerful and dangerous entity that Kakashi believed could only be stopped by killing Naruto.
In fanfiction, Naruto might kill Konoha if he's under some sort of mind control. Maybe an enemy manages to manipulate his thoughts and turn him against the village. Also, if Naruto experiences a great loss because of Konoha's actions or inactions. Say, if his friends are killed due to Konoha's negligence in protecting them, and he blames the village as a whole. Or if he realizes that Konoha's system is so corrupt that it's causing more harm than good to the world.
One possible motive could be if Sasuke was on a path of destruction that endangered the entire ninja world. Naruto, as the protector of peace, might see killing Sasuke as the only way to stop him. For instance, if Sasuke was about to unleash a powerful and uncontrollable jutsu that would wipe out many innocent lives.
Maybe in a fanfiction where Kakashi is mind - controlled. It could lead him to harm Naruto without his normal self - control.
One possible motive could be if his brother was somehow a threat to the village. Naruto is very loyal to Konoha, so if his brother was planning to destroy it or harm its people, Naruto might feel compelled to stop him at all costs.
If such a fanfiction exists, a possible motive could be some kind of mind - control. Maybe an enemy uses a powerful genjutsu on Naruto, causing him to lose his sense of self and attack his mom. But this is still a very far - fetched and unethical concept within the Naruto world.
Jealousy could be a motive. Maybe Naruto's growing power and popularity within the village make his family members jealous. So they decide to kill him to end his rise.