Well, the Dursleys were extremely cruel to Harry. They locked him in his cupboard under the stairs for a long time. They also tried to prevent him from knowing about his magical heritage, which was a big part of who he was. Harry must have felt a great deal of resentment towards them for suppressing his true self.
The Dursleys were always mean to Harry. They gave all the love and attention to their own son Dudley while neglecting Harry. They made him wear Dudley's old clothes which were often too big or too small. They also made him go without proper meals at times. All these unfair treatments would surely make Harry hate them in the fanfiction.
One possible reason could be his lingering resentment towards James Potter, Harry's father. Snape and James had a long - standing feud during their school days. Since Harry looks a lot like James, Snape might be transferring his old grudges onto Harry.
It might show the constant power struggle between them. Harry, as a wizard, has an inner strength that the Dursleys try to suppress with their mundane and cruel ways. So it's a battle of wills.
One reason could be that he discovers a new threat and decides he can't stay with the Dursleys any longer for their safety. Another might be that he simply can't bear their mistreatment anymore and finds an opportunity to escape.
Perhaps he gets a chance to attend a special magical school or training program that requires him to leave the Dursleys. It could be a place where he can develop his powers without the Dursleys' interference. Also, he may be running away from a threat that the Dursleys are unable or unwilling to protect him from.
Some authors might create it as an exercise in 'what - if' scenarios. They want to break the established narrative and see how different characters would react if Harry was killed so early. Also, it could be a way to explore the Dursleys' characters more deeply, showing just how far their hatred for Harry could go.
Well, in some versions of the 'Dursleys abandon Harry fanfiction', they abandon him due to social pressure. They are worried about what their neighbors or friends might think if they find out about Harry's true identity. Also, Petunia may have some deep - seated jealousy towards her sister Lily for being a witch, and this negative feeling extends to Harry, leading them to abandon him.
One possible reason could be jealousy. Maybe the sister is getting more attention from their parents or at Hogwarts. For example, if she is a star student and Harry feels overshadowed.
Another possibility is that there is some sort of personal misunderstanding between them. Maybe Susan Bones accidentally reveals one of Harry's secrets or makes a wrong assumption about him in public, which embarrasses Harry and leads to his hatred. Also, it could be that her family background or family connections play a role. If her family has some past issues with Harry's family or friends, it might fuel Harry's negative feelings towards her.
One consequence could be that Harry becomes withdrawn. He's so used to the abuse that he doesn't trust people easily. He might have nightmares often, reliving the moments of abuse. For instance, if Vernon has hit him before, he could have flashbacks in his sleep.
One popular 'Harry Hates the Dursleys' fanfiction could be 'The Dursley's Worst Nightmare'. In this fic, Harry finally stands up to the Dursleys in a very assertive way. He uses his magic not to harm them but to make them understand how much they've wronged him.