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.
Well, in the original story, Harry's parents are seen as heroes. But in this fanfic, the whole dynamic is flipped. It's a big deviation as it changes the fundamental view of his parents.
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.
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.
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.
Often, it's shown through his internal thoughts. The writer might describe Harry having angry and bitter thoughts about his parents when he's alone, like constantly thinking about how they left him to face so many difficulties. For example, he may think 'My parents left me to deal with Voldemort, they didn't care.'
Obviously, Harry Potter is the main character as he is the one trying to save his parents. His parents, James and Lily Potter, would also be important characters even though they are the ones being saved. There might also be other characters like Dumbledore. Dumbledore could play a role in guiding Harry in his mission, either by providing advice or by giving him some magical tool or knowledge that helps him in his quest to save his parents.
Well, it could be that Harry meets his parents through some magical time - turner accident. Maybe he's on a mission in the past and stumbles upon them.
It could be that his parents were trying to protect Harry in a really messed - up way. They might have thought that by 'betraying' him, like sending him away or making him seem like an outcast, they could keep him safe from a much greater threat. Maybe they knew some prophecy about Harry and thought this was the only way to ensure his survival. They might have made a deal with some dark force, believing they could outwit it in the end but ended up being seen as traitors by Harry and others.