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.
In the original series, Harry is an only child, so the very concept of a sister is a huge deviation. This changes the family dynamics completely. Instead of just having the Dursleys as his only family situation outside of Hogwarts, now there is this sister factor.
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.
He might openly oppose their policies. For example, if the Ministry tries to pass a law that restricts the use of certain spells for self - defense, Harry could publicly speak out against it, giving interviews or writing articles in wizarding newspapers.
Well, this kind of fanfiction might be an interesting take on the character. It could explore a darker side of Harry Potter that we don't often see in the original series. Maybe the author wants to show how all the pressure and trauma he has endured could lead to a more cynical view of those around him.
One possible reason could be the way the Dursleys treated him. They were cruel, made him live in a cupboard, and constantly belittled him. This kind of mistreatment over the years could easily lead to hatred. Another aspect could be the lack of connection to his wizarding family that he was not aware of for a long time. He might feel angry at his parents for leaving him in such a situation without any real protection from the Dursleys.
It completely flips the usual narrative. In the original story, Harry has a sense of longing for his family, especially his parents. But in this fanfiction, the hatred changes the emotional core. It makes Harry a more complex and perhaps darker character. The relationships that were once sources of strength, like his connection to his parents through their sacrifices, now become sources of bitterness.
Obviously, Harry Potter himself is a central character. His sister would be the new addition. Hermione and Ron are likely to be there as well. They are Harry's best friends in the original series and would probably play important roles in the fanfiction too. Dumbledore might also appear, as he is a very important figure in the wizarding world and could guide the sister in her magical journey.
If such fanfiction exists, it may lead to a lot of negative impacts. It can mislead some young and inexperienced readers into thinking that abnormal relationships are acceptable. Moreover, it might face legal issues in some cases as it violates ethical and moral boundaries. Also, it will be shunned by the vast majority of the legitimate Harry Potter fandom who uphold the positive values of the series.
One possible reason could be the Ministry's corruption. In the original series, we saw some Ministry officials being more concerned with power and image than doing what was right. They often turned a blind eye to real threats like Voldemort's return in the beginning. So in the fanfiction, this corruption might be exacerbated, leading Harry to hate the Ministry.