There are several possibilities. One is that he has some sort of internal conflict. Perhaps he's discovered something about his powers or his past that he doesn't know how to deal with. It could also be that he's been betrayed by someone he trusted. Percy has a big heart, and if someone he thought was a friend turns against him, it would be very painful. And of course, it could be related to his relationship with Annabeth. Maybe he's worried about losing her or thinks he's not good enough for her.
It could be that he's lost someone important. Percy has had many friends and family in his life, and if he loses one of them, it would be a huge blow.
It could be that she's homesick. Despite all the adventures, sometimes the longing for home can be overwhelming. Percy would comfort her by sharing his own feelings of missing his mother and how they can make new homes with their friends. He might hold her hand and tell her that their friends are like family now.
She might be initially shocked. After all, seeing someone's abs unexpectedly can be a bit of a surprise.
One possible plot could be extreme embarrassment for both. Percy might quickly turn away and then there could be a lot of awkwardness between them for a while. They would probably have to have a conversation about boundaries and respect.
Perhaps he's feeling guilty about something that happened during one of his quests. Maybe he made a decision that had negative consequences for someone he cares about, and that's weighing on him. It could also be that he's just had a really tough encounter with a powerful enemy and is letting out the pent - up stress and fear through crying.
One possible reason could be miscommunication. Maybe Annabeth made a decision without consulting Percy in the fanfiction, and Percy felt left out or betrayed, leading to his screams.
Perhaps Percy refuses to take on a certain task that Annabeth believes is crucial. It could be something related to saving a friend or retrieving an important item. His refusal might seem cowardly to Annabeth, without her realizing that Percy has some other valid concerns or reasons for not doing it right away.
One alternative could be fanfiction about their adventures together. For example, they could be exploring a new and mysterious realm, facing challenges and relying on each other's skills and friendship. Another option is writing about their character growth, like how Percy becomes more confident in his leadership skills and Annabeth in her wisdom, and how they support each other in these aspects.
One possibility is that it could lead to some awkwardness between them for a while. They might avoid each other's eyes and have stilted conversations until they finally talk about what happened and clear the air.
In this fanfiction scenario, when Annabeth sees Percy on the field trip, it could be a moment full of unspoken emotions. She might be initially hesitant to approach him, but her curiosity gets the better of her. Once they start talking, they could discover that they are both there for a very similar reason related to their demigod world, like looking for a hidden artifact in the location of the field trip.
One possibility is that Annabeth challenges Percy to a little competition related to the field trip. For example, if they are at a museum, they could see who can find the most interesting historical fact about an exhibit first. This would be a fun and friendly way for them to interact and also show off their knowledge.