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.
In this 'Snape kills Harry' fanfiction, it could be that Snape has his own agenda for power. He might think that with Harry out of the way, he can gain more influence in the wizarding world. He could also be driven by jealousy. Maybe he sees Harry getting all the attention and praise, and in a moment of weakness and rage, he decides to end Harry's life.
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 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.
One possible motive could be a severe misunderstanding. Maybe Harry is tricked into believing that Snape and Moody are involved in some dark plot against him or his friends. For example, if there were false evidence planted that made it seem like they were working for Voldemort again. Another reason could be that he was under the influence of a powerful dark magic that clouded his judgment and made him act out of character.
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.
Another motive might be related to a dark object influencing her. If Hermione came across a cursed object, like a dark locket that amplified negative emotions such as envy or fear, it could drive her to kill Harry. Maybe she started to envy Harry's fame and the special attention he always got, and the locket pushed her over the edge.
One possible motive could be his love for Harry's mother, Lily. Even in the fanfiction, this could be a driving force. He might see helping Harry as a way to atone for his past actions towards Harry.
Maybe in some fanfictions, Draco is driven by a sense of self - preservation. He might believe that Harry will eventually turn against him or the Slytherin house. He could think that by killing Harry, he can secure his own place at Hogwarts and in the wizarding community. Additionally, it could be part of a larger plot by Voldemort or his followers. If Draco is forced to join Voldemort's side, he may be given the task of killing Harry to prove his loyalty.
Maybe Fudge was starting to turn against the wizarding community in more extreme ways. For example, if he was planning to persecute Muggle - borns more harshly or side with the Death Eaters secretly. Harry, being a defender of justice and equality in the wizarding world, would not tolerate such actions and might have been pushed to kill Fudge to stop his evil plans.
In some fanfictions, Snape could have his own personal vendetta against Dumbledore. Maybe Dumbledore has wronged Snape in the past, and when he sees Harry as a potential victim of Dumbledore's schemes, he decides to help Harry. Another reason could be that Snape has a new understanding of the prophecy and believes that Dumbledore's way of handling it is wrong, so he steps in to help Harry.
One possible motive could be Snape's complex relationship with Harry's father. Snape might see Harry as a way to get back at James in some twisted way. He could also be acting out of a sense of duty to the Dark Lord, believing that taking Harry by force is part of some larger plan to gain power or favor.