It might be that the high school setting in the fanfiction is too clichéd for her. Annabeth is a complex character and perhaps she feels that the typical high school drama scenarios in the fanfiction don't do justice to their story. For example, if it reduces their epic adventures to simple high school rivalries, she would likely hate it.
Another reason could be that the fanfiction doesn't respect the growth and development of their relationship. Annabeth and Percy have a deep, evolving bond. If the fanfiction simplifies it or takes it in a direction that doesn't align with how their relationship should progress, it would make her dislike it.
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.
Maybe she's jealous of Percy's popularity at school. It could be that he always gets more attention, whether it's from teachers or other students.
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.
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.
It could be shown through his avoidance. He might always try to stay away from Annabeth in the hallways or during group activities.
One possible reason could be competition. Annabeth is highly competitive and Percy's sudden appearance and his own skills might make her feel threatened, leading to hatred. For example, if he outperforms her in a training session or a quest task.
One possible reason could be jealousy. Maybe Rachel has something that Annabeth wants, like a closer relationship with a particular character. For example, if they both like the same guy, Annabeth might hate Rachel out of envy.
Love is a big reason. She loves Percy deeply and is afraid of losing him. In the world of the fanfiction, there could be many threats to their relationship, so she holds on tightly.
One possible reason could be her deep love for Percy. She might see his life as more valuable in the grand scheme of things, perhaps because of a prophecy or a mission that only he can complete. So, she chooses to sacrifice herself to ensure his survival.
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.
It could also be due to some sort of magic or mind - control. A powerful enemy might have cast a spell on Annabeth, forcing her to turn against Percy. In this case, it's not really her own will but the result of external manipulation.