One possible reason could be that she suspects Percy has some sort of mark or injury on his torso. Maybe they were in a recent battle or encounter and she wants to check if he's okay.
In the context of a fanfic, there could be a bet or a dare involved. Percy lost a bet or was dared to let Annabeth take his shirt off. This could lead to some humorous or interesting interactions between them as they both deal with the situation.
One possible scenario could be that Percy got injured and Annabeth needs to tend to his wounds on his torso, so she takes his shirt off. For example, he might have been scratched by a monster during a battle, and she has to clean and bandage the wound quickly.
A reason could be that he's overheating. Danny's powers might sometimes cause his body temperature to rise, and taking off his shirt helps him cool down. It's a simple practical reason that could be used in a fanfiction to show his more human side, dealing with the physical discomforts that come with his ghostly powers.
It could be a story where Percy takes his shirt off during a training session. Maybe he's getting ready for a really intense sparring match and removing his shirt is part of his pre - fight ritual to show his determination and focus.
Annabeth could be one of the main characters interacting with him. She might tease him about taking his shirt off, or she could be concerned if he's taking it off because of an injury. Their relationship is complex, and this situation could add a new layer to it.
He could be a bit shy. Since he also has feelings for Annabeth but was too nervous to make the first move. So when Annabeth asks him out, he blushes and stammers a bit, like, 'Uh, yeah, Annabeth. That sounds great.' And then he would be really happy inside, thinking about all the things they could do together on their date.
Well, perhaps Percy plans this elaborate scheme to ask Annabeth out. He might enlist the help of their friends, like Grover. Grover could set up a picnic in a beautiful meadow. Percy then shows up with a bouquet of Annabeth's favorite flowers and asks her out. She would be touched by the effort he put in and say yes. Then they start planning all the things they want to do together on their first official date.
One possible place could be in the Underworld. It would be a very unexpected and dangerous place, but that would add to the drama. They might be there on a quest and find a moment of peace and passion among the chaos of the dead.