It could be due to a sense of abandonment. Fanfic writers might explore the idea that Harry, growing up without his parents, feels resentful. He may see other kids with their families and, in his confusion and pain, start to hate his parents for leaving him alone in the world, even though it was not their choice.
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.
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.
Yes, there might be. Some fanfics like to subvert the expected negative situation. In these fanfics, even though the start is that Harry's parents hate him, through a series of events such as Harry showing extraordinary courage or kindness, his parents could have a change of heart. For example, he might save them from a great danger, which makes them realize their mistake and start to love him. This kind of plot twist can add more depth and surprise to the fanfic.
In these fanfics, a common theme is growth. Harry has to grow up faster and become more independent because of his parents' hatred. Another theme is the search for identity. Without the positive influence of his parents, he has to define himself. And the theme of resilience is also prominent. Harry has to be strong in the face of his parents' negative feelings and all the difficulties that come with it. He has to keep going and not let their hatred break him.
In some fanfictions, Naruto might be depicted as hating his parents. However, this is a departure from the canon. In the original Naruto story, Naruto grows to understand and respect his parents as he learns about their sacrifices. But in fanfiction, authors can take creative liberties and explore different emotional states for Naruto towards his parents, such as hatred perhaps born out of feeling abandoned, even if it goes against the essence of the original story.
At the start, Harry would be stunned. His whole life has been built on the idea of his parents being heroes. When he realizes they betrayed him, he would be heartbroken. He might go on a journey to find out the real motives behind their actions. Along the way, he could become bitter and vengeful. However, he might also find some inner strength and decide to rise above the betrayal. He could use it as a motivation to break free from the shadows of his parents and create his own path, but not without a great deal of emotional turmoil first.
One possible reason could be that Naruto has some sort of power within him that they fear. Maybe it's a power that they don't understand and think could be dangerous, so they hate him out of fear.
One possible reason could be that in the fanfic, his parents might be depicted as having made some big mistakes in the past that directly affected Harry in a negative way. For example, they could have made a deal with a dark force that put Harry in danger later on.