What was the cause of the quarrel between Agamemnon and Achilles?

When the king agrees to return Chryseis without accepting any ransom and to give a hundred sacred bulls for sacrifice, he says 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, 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.