Well, it's a disturbing topic. Sometimes, the caregivers might have untreated psychological disorders that lead them to such heinous acts. Or, maybe they are in a desperate financial situation and see it as a way out. Another factor could be a lack of proper support and resources, causing them to snap.
A common motive could be the pursuit of power. Vampire children may be tired of being under the control of the head vampire parent and see killing them as a way to gain absolute power within the vampire hierarchy.
Revenge can play a role too. If one friend feels wronged by the other, maybe through an act of betrayal or a hurtful comment in the past, they could seek revenge in the most extreme way, which is murder.
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.
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.
In some fanfics, a motive could be a deep - seated jealousy. Suppose Steve gets all the glory and recognition while Bucky feels left in the shadows. This could build up resentment over time and lead to a situation where Bucky snaps and kills Steve. However, this is a very different take from their normal relationship in the official stories and really plays with the emotions and expectations of the readers.
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 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.
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.
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 he wants to change the system. Percy has always been a bit of a rebel, and in fanfiction, he could see the gods' rule as corrupt or unfair. So, killing them could be his way of starting anew and creating a better world for demigods and mortals alike. Another motive could be to prevent a greater evil. If he discovers that the gods are planning something that would destroy the world, he might decide that killing them is the only way to stop it.