In Percy Jackson and the Olympians: the Lightning Thief by Rick Riordan, the plot centers on a world where Greek gods and goddesses exist and have children. The children of the Greek pantheon are demigods, and they possess some of the powers of their parents. Those demigods operate similarly to the demigods of mythology—they are heroes, and they go on quests.
Percy is unique because he is a son of one of the three principal gods in the mythology. Poseidon claims Percy as his son at the end of Chapter 8. Percy’s team at Camp Half-Nlood just won the game of capture the flag they were playing. Suddenly, a hellhound appears from nowhere to attack Percy. He is injured, but the hound is killed. Annabeth, a daughter of Athena, tells Percy to get into the water because she has a theory that he will be healed.
“Oh Styx,” she cursed.“This is not good. I didn’t want . . . I assumed it would be Zeus . . .” (Page 124)
This passage shows that Annabeth is upset with Percy, as you mentioned, but it doesn’t explain why. It also shows us that Annabeth is smart—no wonder, as she is the daughter of the goddess of wisdom—because she figures out that Percy is the son of Poseidon from his use of water for healing. With his father's claim, Percy is moved out of the traveler cabin 11 and into the Poseidon Cabin 3.
We find out in the next chapter of the book the specific reasons why Annabeth is upset. First, we get some foreshadowing—after Annabeth provides Percy with lessons in Greek she says,
“Quest . . . Poseiden? . . . Dirty rotten . . . Got to make a plan . . .” (Page 128)
Annabeth’s anger at Percy is partially old because of her inability to get a quest and partially new because of the revelation that Poseidon had a child—something he is not supposed to do. She tells Percy later in the chapter the exact reason,
“I’ve been waiting a long time for a quest, seaweed brain,” she said.“Athena is no fan of Poseidon, but if you’re going to save the world, I’m the best person to keep you from messing up.” (Page 147-148)
Annabeth is upset because quests were banned for a time at the camp after Luke failed one miserably. Annabeth has wanted a quest for a long time to prove herself to her mother and gain some attention from Athena. Percy, a new demigod, shows up, and suddenly he gets a quest just because of his father. That grates on Annabeth.
Something else she mentions, which comes into play later in the story, is that Poseidon and Athena are not friends, and their children aren’t supposed to be either. It goes back to an old myth about their rivalry to become the patron god of Athens. Athena won, giving them the olive tree, and ever since they have been at odds with one another. Annabeth bucks that trend, falling in love with Percy eventually, but it is one example of how Riordan weaves the old myths into the new story and makes them relevant.