It could be that their personalities clash. Annabeth might be very logical and organized, while Rachel could be more free - spirited and spontaneous. This difference in their ways of being might lead to Annabeth disliking her. For instance, Annabeth's plans might be constantly disrupted by Rachel's impulsive actions.
Perhaps there have been some misunderstandings between them. Rachel might have accidentally done something that Annabeth misinterpreted as a hostile act. Say, Rachel took something that Annabeth thought was hers without realizing it was important to Annabeth, which could start the hatred.
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.
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.
Well, perhaps Rachel has some unique talents or abilities that catch Percy's attention. In the fanfiction, this might make Annabeth feel insecure about her own relationship with Percy. For example, if Rachel can communicate with the gods in a way that Annabeth can't, and Percy is impressed by it, Annabeth could get jealous.
Well, it could be about different understandings of Percy. Annabeth knows Percy as a demigod, as a hero in their world. Rachel, on the other hand, might see Percy in a different light, more as an individual outside of the demigod stuff. They might fight because they both think they know what's best for Percy and how he should be. Also, it could be a fight for Percy's future. Annabeth might want Percy to stay in the demigod world and continue their adventures together, while Rachel could have different plans for him.
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 reason could be that Rachel represents a different world to Percy. She's more of an outsider to the demigod world, and Percy might be attracted to that sense of newness and freedom she seems to offer. Maybe he's tired of the constant danger and drama in the demigod life with Annabeth.
Often, it starts with small incidents that show Annabeth's dislike. For example, she might give Rachel cold looks or make snide remarks. Then, as the story progresses, the tension builds. Maybe they end up competing in some way, like for a leadership position in a group.
She could be heartbroken. Annabeth has been through a lot with Percy, and to be rejected for Rachel might make her feel like all their adventures together meant nothing.
It could also be due to a misunderstanding. Kakashi might be keeping some secrets from Naruto, like information about his parents or some hidden power within him. Naruto, being curious and eager for answers, could misinterpret Kakashi's motives for secrecy as a sign of distrust or dislike, which then turns into hatred.