It was Annabeth's own quest, too. She is just jealous that she has to do stuff like punch Percy and tell him to ask her for a dance, stalk him all the way to his home to get to know stuff about him and find a quest to spend time with him, while Rachel just meets him twice and immediately gets his trust.
She gives him her number and Percy memorizes it, accepts her painting of him as a gift and shows initiative in spending time with her and going on a date with her, while Annabeth's wondering how Percy could be so blind and hurtful to her and her advances. The said advances include her being aggressive with him, passive-aggressive with him, demeaning his intelligence; constantly defending his enemy and not hearing his side of it, and immediately blaming him for things he had no control over.
Like Rachel who has met Percy for barely two minutes knows Percy couldn’t have done anything about being attacked at school and offers to cover for him while Annabeth immediately gets angry at him and puts the blame on him when she knows the situation could not have been instigated by Percy. This is one of the many examples.
I know Percabeth is considered a gold standard among ships, but I will never be able to see it.
Annabeth: *calls Percy impossible for not being in the mood to empathise with a guy who's tried to kill him multiple times the last time being five minutes ago and then immediately insults the girl who's risking her life to help them just because she's territorial over the guy she refuses to confess her feelings to*