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.
She might be possessive because of her own insecurities. Maybe she feels that other girls are better than her in some ways, like being more beautiful or having different skills, and she's worried Percy will be attracted to them.
Well, it could be shown through her getting jealous easily when other girls interact with Percy. For example, if a new girl in the story tries to talk to Percy, Annabeth might give the girl a cold stare or quickly insert herself into the conversation.
Love could be the main reason. Since he loves Annabeth deeply, he doesn't want to lose her, so he becomes possessive.
In the fanfiction, Percy's possessiveness might also be demonstrated by his need to be included in all of Annabeth's plans. He may feel left out or threatened if she starts making plans with other people without him. He wants to be a part of everything she does, almost like he owns a part of her time and attention.
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.
Well, one possible reason could be that Percy made a really stupid decision without consulting Annabeth first. Like, if he went off on a dangerous mission on his own when they were supposed to be a team. Annabeth is a very strategic person and she might feel betrayed or extremely frustrated by such actions.
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.
Maybe she's scared because the fanfiction portrays Percy in a way that's out of character for him. Like, it might show him being overly aggressive or having strange powers that she doesn't recognize, which makes her feel like she doesn't really know him anymore.
It could also be that in the fanfiction, Percy is given a new power or ability that Annabeth sees as a threat. Or perhaps Percy is made to side with someone Annabeth dislikes, causing her to 'hate' him in that fan - created story. This shows how different plot elements in fanfiction can change the dynamics between characters.
Perhaps the fanfiction is set in an alternate universe where something has happened to change Percy's feelings towards Annabeth. For example, if there was a betrayal in the fan - created story that made Percy turn against her.
One possible reason could be a misunderstanding. Maybe she saw Percy doing something that she misinterpreted as a betrayal of their friendship or their cause. For example, if Percy was seen talking secretly with an enemy, Annabeth might jump to conclusions without knowing the full story.