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.
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.
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.
Another way is through the intervention of their friends. Their mutual friends could bring them together and encourage them to see things from the other's perspective. The friends can share stories about how each of them is really a good person deep down. This might soften their hearts towards each other.
The author of the fanfiction could rewrite it to better align with the characters' personalities. For example, by making Percy more in - character and the high school setting more unique.
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.