It could be due to a misunderstanding. Perhaps there was an incident where the sister was involved, but Harry misinterpreted her actions. Say, she was trying to protect him but it came across as something else.
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.
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.
One possible reason could be a misunderstanding. Maybe Lupin did something that Harry misinterpreted as betrayal or negligence. For example, if Lupin was forced to keep a secret from Harry for his own safety, but Harry found out in a way that made him feel deceived.
One possible reason could be that fanfiction often takes creative liberties that may distort the complex character of Snape that J.K. Rowling created. Snape has a very intricate backstory and personality in the original series, and fanfiction might simplify or misinterpret it.
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 possible reason could be that in the fanfiction, her parents might have made a sacrifice that left her alone, and she resents them for not being there for her. Maybe she feels abandoned and that has led to her hatred.
One possible reason could be the betrayal he faced from some people in the wizarding world. For example, some students at Hogwarts might have spread false rumors about him or treated him unfairly because of his fame as 'The Boy Who Lived'. This could have led him to develop a general dislike for humans.
In this fanfiction, perhaps there's some miscommunication. Maybe the Weasleys' boisterous nature is misconstrued by Harry. For example, their large family dynamic might be overwhelming to him at times, which could be a reason for the 'hate' in the fanfic.
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.
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.
One possible reason could be a miscommunication. Maybe Hermione accidentally reveals a secret of Harry's that he didn't want known, and this causes him to feel betrayed and start to hate her. Another reason could be jealousy. If Hermione gets more attention or praise for her magical abilities than Harry in the fanfic, he might develop feelings of envy and hatred. Or perhaps there's a love triangle situation where Hermione is involved with someone Harry doesn't like, and that causes his hatred.