Differing ideologies during the wizarding war. If James was seen as a threat to Snape's side (even if Snape was on the wrong side, from a moral perspective), Snape could justify killing him. For example, if James was too aggressive in fighting the Death Eaters and Snape thought it would lead to more bloodshed, he might take matters into his own hands to stop James.
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 motive could be a misunderstanding. Maybe Snape is framed for something really bad, like a dark magic plot against Hogwarts. Harry, in his haste to protect the school and his friends, believes Snape is guilty and takes drastic action. Another reason could be if Snape accidentally endangers someone Harry loves dearly, like Ginny or Ron, and Harry's emotions get the better of him in the heat of the moment.
Perhaps in the fanfic, Snape discovers a powerful and dangerous magic that he wants to use for what he believes is the greater good, but Harry sees it as a threat. Harry has always been wary of Snape, and this new discovery could be the tipping point. Also, if Snape were to make a deal with a dark force in order to gain knowledge to defeat Voldemort but Harry misinterprets his intentions, it could lead to Harry killing Snape.
One possible motive could be jealousy. Snape might be really good at certain subjects like potions, and the Marauders, being competitive, might bully him to make themselves feel better.
One possible motive could be revenge. The Dursleys treated Harry awfully for years, so in fanfiction, he might reach a breaking point. Another could be self - defense if the Dursleys in the fanfiction were to take their abuse to an extreme level.
One possible motive could be jealousy. Hermione is highly intelligent and often outshines Draco in academics. In a twisted version of a rivalry, Draco's envy could turn into a deadly hatred. Another could be his family's influence. If the Malfoys push him to take extreme actions against Muggle - borns, Hermione would be a prime target.
A possible motive could be revenge. If a dragon had hurt someone he loved, like his father or Astrid, he might be driven to kill it. It would be a very emotional and difficult decision for him, but his love for his friends and family could push him to that extreme.
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.
Power. Voldemort might see Snape as a means to gain more power. Snape is highly intelligent and skilled in the Dark Arts. By caring for him, Voldemort could be ensuring that Snape remains loyal and continues to use his skills for Voldemort's benefit.
Perhaps Stiles discovers some dark secret about the alpha pack that endangers the entire town or the supernatural world he's a part of. In his sense of responsibility and his unique way of thinking, he figures that killing the alpha pack is the only solution to prevent a greater catastrophe. This can add a lot of depth to the fanfiction story, exploring Stiles' moral compass and his ability to make tough decisions.