Perhaps Percy forgets an important promise he made to Annabeth. In their relationship, promises are significant. If he fails to keep one, like a promise to help her with a project or be at a certain place at a certain time, Annabeth would surely be mad. It could also be that Percy accidentally breaks one of Annabeth's creations or possessions, which she holds dear.
In some fanfiction, Percy might make a decision that goes against Annabeth's beliefs or values. For instance, if he decides to use a method that Annabeth considers unethical to solve a problem. This difference in views can lead to Annabeth getting angry. Also, if Percy undermines Annabeth's authority in a group situation, that would definitely make her mad as she is a strong - willed character who values her leadership.
Perhaps Percy made a decision without consulting Annabeth. In many fanfictions, Annabeth values being part of the decision - making process, especially when it concerns their relationship or a mission they're on. If Percy went off and did something like made a deal with a potentially dangerous character on his own, Annabeth would be furious.
One reason could be that she's scared. The idea of becoming a mother at that point in her life might be overwhelming, and she might think she can't handle it with Percy. Maybe she wants to protect Percy from the difficulties that come with the pregnancy as well.
One possible reason could be a misunderstanding. Maybe Annabeth made a decision without consulting Percy, like choosing a quest that she knew was dangerous but didn't tell him until it was too late. Percy might feel left out and mad about it.
Annabeth could be under some kind of magical influence. In the Percy Jackson universe, there are many magical elements. She could be cursed or charmed without her knowledge. This would be a very interesting take in a fanfiction as it would add an element of mystery and also give her a chance for redemption once the truth is discovered. Also, it could be that she has some internal insecurities that she hasn't dealt with and they manifest in this way, making her act out of character.
One possible plot could be that Percy gets mad because his friends don't believe him about a new threat he has discovered. He might storm off and try to face the threat alone, leading to all sorts of dangerous situations.
It can strain their relationship. When Annabeth is mad, there will be tension between them. They might not communicate as effectively, which could lead to misunderstandings. For example, if Percy doesn't understand why Annabeth is mad, he might say or do the wrong things, making the situation worse.
Annabeth is a very determined and strong - willed character. In her mind, Percy is part of her 'territory' because she has fought beside him and for him. She may feel that she has a claim on him, and this sense of ownership makes her territorial.
In some fanfictions, Annabeth could abandon Percy because of a prophecy. If the prophecy seems to imply that being with Percy will lead to a great disaster, she might choose to leave to protect him or the world. Also, it could be due to a personal growth arc for Annabeth. She may realize that she has been too dependent on Percy in the past and decides to go off on her own to find her true self, leaving Percy behind.
One possible reason could be a misunderstanding. Maybe Percy did something that Annabeth misinterpreted, like being overly friendly with another character which made her jealous and led to her rejection.
One reason could be a shift in the plot where Annabeth's character development leads her to realize she and Percy are not compatible in the way they were initially thought. Maybe she has new goals or a different understanding of herself that makes her feel she's better off without Percy in the fanfiction world.