Perhaps Annabeth's dad has some old - fashioned ideas. He might believe that Percy doesn't have the right qualities to be with his daughter. He could also be jealous in a way. Percy is an important person in Annabeth's life and her dad might feel left out or that Percy is taking his place in a sense.
One possible reason could be jealousy. Maybe Percy gets more attention or recognition in their fictional world that makes Annabeth envious and thus appear to hate him.
Well, at first, Annabeth's dad might be quite hostile. He'd be worried about his daughter getting involved with someone like Percy who is constantly in danger. But if Percy shows his loyalty to Annabeth and his good nature, like by being polite and showing respect for Annabeth's family, her dad could gradually change his attitude. Maybe he'd start to see Percy as a brave young man who can protect Annabeth rather than a threat.
One possible reason could be that the fanfiction misrepresents their characters. Maybe it portrays Percy in a way that Annabeth doesn't like or goes against the essence of their relationship as she sees it.
One possible reason could be a misunderstanding. Maybe Percy did something that Annabeth misinterpreted, like making a decision during a quest without consulting her first, which made her feel disrespected.
They could have an honest conversation. Just sit down and talk about their feelings and misunderstandings. This simple act can clear the air and resolve the hatred.
In the fanfiction world, when Percy meets Annabeth's dad, it could start off rocky. Her dad might be overprotective and see Percy as a threat to Annabeth's normal life. However, as they talk, Percy could share his heroic tales, not to brag but to show that he has the strength and courage to protect Annabeth. Annabeth's dad might then start to warm up to Percy, realizing that he is more than just a trouble - making demigod. Percy could also learn a lot about Annabeth's family background from her dad, which would strengthen his bond with her.