One possible motive could be his intense hatred for the wizarding world. Since Harry represents that world to him, he might murder someone he believes is part of the magic that he despises so much. Another motive could be fear. If he feels threatened by a magical being or situation, in his panicked state, he could resort to murder.
A possible motive for Vernon to murder in fanfic could be self - preservation. He might think that by getting rid of a certain character, he can protect his family from the perceived danger of the wizarding world. He could also be motivated by pride. If his reputation or status in the muggle world is at stake because of some magical interference, he might murder to keep his standing. Additionally, if he discovers some dark secret about the wizarding world that he wants to keep hidden, he could murder to silence someone who knows it.
In most of the official 'Harry Potter' canon, Vernon Dursley didn't murder anyone. However, in fanfic, the story can take many wild turns. It depends on the specific fanfic in question. Some fanfics might create extreme scenarios where Vernon could be involved in a murder, perhaps out of his extreme dislike for magic or a character related to magic. But without reading the particular 'Harry Potter Vernon murdered' fanfic, it's hard to say for sure.
One motive could be that Voldemort wants Harry on his side. He might think that by rescuing Harry from Vernon, who was clearly a bad caretaker, Harry would be more inclined to listen to him and join him.
One possible motive could be to explore a dark and alternate universe. The writer might want to see how the 'Harry Potter' world would change if such a drastic event occurred. Another reason could be to analyze the characters from a different perspective. By making Harry the destroyer of Dumbledore, it forces readers to re - evaluate both characters.
Perhaps Fleur is being controlled or influenced by a dark force. In the Harry Potter universe, there are many dark magic entities that could manipulate someone into kidnapping Harry. It could be that she is under the Imperius Curse or some other form of mind control. Another reason could be that she has some sort of personal vendetta against Harry or those close to him, and kidnapping him is her way of getting revenge. She might think that Harry has wronged her in some way, whether it's real or just in her deluded perception.
In a 'Harry framed Dumbledore' fanfic, a motive could be revenge. Suppose Dumbledore made a decision that Harry thought was wrong and cost someone Harry loved dearly. Harry could then be driven by revenge to frame him. Also, it could be a case of Harry being under the influence of a dark force. The dark force might convince Harry that Dumbledore is a threat and needs to be removed from power, leading Harry to frame him.
In this fanfiction scenario, it could be that the writer decided to change the power dynamics completely. Vernon, who is usually just a Muggle bully in the original, might be given some unexpected power or weapon in the fanfic. And Harry, perhaps caught off - guard or having lost his magic temporarily, could be killed by Vernon. It shows how fanfiction can turn the whole story upside down.
In this kind of fanfiction, perhaps Harry, out of fear or some form of coercion, starts to obey Uncle Vernon's every order. Maybe Vernon uses threats about expelling Harry from the house or withholding food to make him submit. This could lead to a very different dynamic in the Dursley household, with Harry being more submissive and not showing his usual defiance.
In the fanfic, perhaps Harry had reached his limit with Umbridge's blatant disregard for the rights and well - being of the students and magical creatures. She was a symbol of the corrupt Ministry at that time. Harry, having a strong sense of justice, could no longer tolerate her presence and actions, especially after seeing how she treated his friends and those he cared about at Hogwarts.
One possible motive could be extreme revenge. After years of being mistreated, locked in a cupboard, and generally being made to feel unwanted, Harry might snap in fanfiction. Another could be a sense of self - preservation if the Dursleys were somehow involved in a plot against Harry's life in the fan - created plot.
Well, one possible motive could be that the assassin is working for Voldemort. Moody was a powerful Auror and a threat to Voldemort's plans. By eliminating him, it would clear the way for the Dark Lord's operations. Another motive might be personal revenge. Maybe Moody had put someone close to the assassin in Azkaban in the past, and this was a way to get back at him.