Well, in some fanfictions, Percy might be mad at Annabeth because of a misunderstanding. Maybe she made a decision without consulting him in a crucial situation regarding their adventures. For example, if she chose a path that put their friends in danger without his input, Percy could get angry.
One possible reason could be a misunderstanding. Maybe Annabeth made a decision without consulting Percy, like choosing a quest path that Percy thought was too dangerous. Percy, being protective and having his own ideas about how things should be done, might get mad.
When Annabeth is mad, Percy will likely try to make it up to her. He might start doing all kinds of things like bringing her favorite foods, trying to help her with her projects. But Annabeth might not be so easily swayed. She'll be looking for a real apology and for Percy to show that he's learned his lesson. So the relationship becomes a bit of a power struggle, with Percy trying to regain her favor and Annabeth deciding whether he's worthy of it.
One scenario could be that Annabeth accidentally revealed Percy's secret identity to someone he didn't want to know. This could put him in danger and make him furious with her.
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.
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.
Let's say Annabeth put Percy's friends in danger without his knowledge. Percy is very loyal to his friends, and knowing that Annabeth's actions could have hurt them would surely make him angry at her.
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.
It could be because of a misunderstanding. In the fanfic, perhaps Annabeth was seen talking to an old acquaintance who Percy doesn't trust. He might jump to conclusions and get angry with her without really knowing the whole story. Like, if he thought she was plotting something behind his back with that person.
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.