Why did Achilles get mad of Agamemnon?

Agamemnon is furious with Calchas, saying that the seer enjoys delivering evil prophecies, but the king agrees to give up the girl. He insists, however, that one of the Achaeans give him a prize to compensate him for his loss.

Achilles is enraged by the request. The plunder has already been distributed, he argues, and a good man does not take back what he has given. Agamemnon and Achilles argue, each man insulting the other. Agamemnon threatens to take a prize if one is not given to him, and Achilles reminds him that all of the Achaeans are fighting against foes who have only wronged Menelaus. For the sake of the two royal brothers, the Argives bloody their hands against men who have done them no wrong. Achilles also complains that though he bears the heaviest burden in battle, it is the king who is always greedy for prizes. Achilles refuses to fight anymore: he will go home to Phthia. Agamemnon responds that to compensate for the loss of Chryseis, he will take Achilles' own prize, the girl Briseis.

Agamemnon, angry that the God Apollo has him give back Chryseis, turns to the second best female mate won from the city, Briseis. Briseis, however, was already awarded to Achilles and this objectified woman is important because she is also a physical representation of his achievement of honor and glory. By taking Briseis away from Achilles, Agamemnon has committed a grave Greek injustice in robbing Achilles of all he had accomplished.