One possible motive could be a conflict over their loyalties. Remus is a werewolf and has his own set of insecurities and allegiances. Maybe Snape discovers something about Remus that he threatens to expose, leading Remus to kill him in a moment of panic. For example, if Snape were to find out about Remus endangering students during his werewolf transformations and was about to report him to the authorities.
In some fanfiction, it might be related to a power struggle within the wizarding world. Suppose there is a secret plot or a fight for control over a powerful magical artifact or spell. Remus could be influenced by dark forces or simply trying to protect something he believes is right. Snape, on the other hand, might be in his way, and Remus sees killing him as the only option to achieve his goals.
One possible motive could be Anakin's fall to the dark side. The dark side clouds his judgment and makes him see Obi - Wan as an obstacle to his power. He might believe that by eliminating Obi - Wan, he can fully embrace the dark side and gain more control. Another motive could be jealousy. If Anakin feels that Obi - Wan is always favored or is holding him back in some way, this could fuel his anger and lead to him wanting to kill Obi - Wan. Also, the influence of Palpatine might play a huge role. Palpatine could have manipulated Anakin into believing that Obi - Wan is a threat to the new order he wants to create.
One possible motive could be to protect Sasuke. Itachi might have seen a great danger approaching Sasuke that he could only avoid by taking him away forcefully. Maybe there was a powerful enemy targeting Sasuke, and Itachi thought that by kidnapping him, he could keep him safe in a hidden location and train him to become stronger.
A possible motive could be revenge. Some characters who have a grudge against Lupin, perhaps because of his association with certain groups or events in the wizarding world, might kidnap him. For example, if a werewolf-hating group found out his identity, they could kidnap him to make an example out of him.
One possible plotline could be that Snape discovers a hidden weakness of Voldemort. Maybe through his years of spying, he finds out that a certain spell, when combined with an ancient magic artifact, can destroy Voldemort. So he devises a plan to get hold of the artifact and uses the spell at a crucial moment when Voldemort is off - guard, perhaps during a major battle when Voldemort is focused on other opponents.
One possible motive could be that Snape is still deeply influenced by his loyalty to Voldemort in this fanfiction. Maybe Voldemort has some hold over him that forces him to do the unthinkable. Another reason could be a misunderstanding. Snape might believe that Harry has turned to the dark side or is about to, and he decides to take preemptive action to stop what he thinks will be a great evil.
One possible plotline could be that Remus and Snape are forced to work together on a special mission within Hogwarts. They initially clash due to their past differences, but as they face various challenges together, they start to respect each other more. Then, they both have a connection with a third character, perhaps a new teacher at Hogwarts. They form an unlikely alliance to protect this person from some dark forces that are emerging in the wizarding world. This new bond gradually develops into a deep friendship that has elements of a threesome relationship in terms of their shared experiences and mutual protection.
It's not a super common theme but it does exist. The motives could also be related to a dark turn in Harry's character. Maybe in these fanfictions, Harry is influenced by dark magic or has been pushed too far by the Dursleys' constant mistreatment. He might see killing them as the only way to break free from the chains of his past. But this goes against the core values of the original series which promotes forgiveness and love in the face of adversity.
One possible motive could be self - defense. Morgana had turned to the dark side and was constantly causing harm to Camelot and its people. Merlin, as the protector of Camelot, might have seen killing her as the only way to stop her reign of terror. For example, she was plotting against Arthur and trying to bring down the kingdom. Merlin's loyalty to Arthur and Camelot could have driven him to this extreme decision.
It could also be a result of some external influence, like a dark magic spell that has clouded Ron's judgment. This spell could be making him act against his normal character and do something as extreme as kidnapping Hermione. However, in the end, he would likely break free from this influence and realize the error of his ways.
In some fanfictions, Snape might be working with Voldemort because he has been blackmailed. Voldemort could have found out some deep, dark secret about Snape and is forcing him to cooperate. This could be related to Snape's past or something he has done that he doesn't want to be made public.