There could be several motives. Firstly, some writers might want to create a high - impact, thought - provoking story. By having Harry's parents kill him, they immediately draw the reader's attention and make them question everything they know about the 'Harry Potter' world. Secondly, it could be an exploration of the nature of good and evil. Even the most 'good' characters in the original series, like Harry's parents, could be made 'evil' in this fanfiction. It might also be a way to show how fragile the concept of heroism is. If Harry, who was destined to be a hero, can be killed by his own parents, it makes the idea of heroism more complex and less straightforward.
Well, it could be for the sake of exploring a different kind of magic or a different set of rules in the wizarding world. Perhaps in this fanfiction's version, the parents were under some sort of dark magic influence that made them turn on Harry. Or it could be a psychological exploration. The writer might be interested in delving into the minds of Harry's parents and seeing what could make them do such a heinous act. It could also be just a very different take on the concept of family and love in the 'Harry Potter' universe.
One possible motive could be that Dumbledore saw a future where Harry's parents' deaths were necessary for a greater good. Maybe he knew that Harry would be the only one to defeat Voldemort in the end, and their deaths were a catalyst to set Harry on that path.
One possible reason could be that he might feel abandoned. Growing up without them, he could resent the fact that they left him an orphan. He might think that if they were really so great, they would have found a way to survive and be there for him.
One possible motive could be jealousy. Maybe the sister is jealous of Naruto's popularity, his strength, or the attention he gets from others in the village.
One possible reason could be a misunderstanding. Maybe he discovers some secrets about his parents that he misinterprets. For example, if he finds out they were involved in some dangerous or morally ambiguous activities in their youth that he doesn't fully understand at first.
One possible reason could be that he discovers some long - hidden family secrets that make him question his parents' actions or decisions. Maybe he finds out about some dark deeds in their past that he can't overlook.
One possible motive could be extreme revenge. If the Muggle relative, like the Dursleys, had been particularly cruel to Harry over the years, some fanfiction writers might explore the idea of him snapping and seeking ultimate revenge. Another could be a dark magic influence. Maybe in the fanfic, Harry is exposed to some dark magic that corrupts his mind and makes him view his Muggle relative as an obstacle to be removed.
One possible reason could be that in the fanfiction, Harry might have discovered some dark secrets about his parents that made him feel betrayed. For example, if he found out they had some hidden and unethical magical experiments in their past.
One possible reason could be that in the fanfic, the author might twist the story to make it seem like his parents' actions had unforeseen consequences that affected Harry negatively. For example, their fight against Voldemort led to Harry being an orphan and having to bear a great burden from a young age.
Perhaps he discovers some secrets about his parents that he doesn't like. For example, he might find out that they were involved in some dangerous or unethical magic before. This new knowledge could make him angry at them for putting themselves and their family in jeopardy.
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.