Agamemnon and Chryses
Homer's Iliad opens not with fighting, but with Chryses, priest of Apollo, entering the Greek camp at Troy to beg Agamemnon for the release of his daughter, Chryseis. The girl, captured by Achilles in a raid, has since become Agamemnon's concubine. Chryses offers a generous ransom which Agamemnon refuses out of hand. Worse, the son of Atreus informs that old priest that he prefers Chryseis to his own wife, Clytemnestra, and cruelly adds that he will take Chryseis home with him, where she will grow old performing menial tasks around the palace by day, while serving him in his bed at night. Agamemnon then has Chryses manhandled and forcibly thrown out of the camp.
Abusing a priest like this was an absolute no-no in the world of the Iliad. Agamemnon's brusque refusal of Chryses initiates not only a deadly plague from Apollo, whose priest Chryses is, but the loss of Briseis and dishonoring of Achilles, and, subsequently, all the disaster to come.
So why does Agamemnon respond to the supplicant priest as he does? Can he truly be that ruthless, single-minded, and foolish, or is there another dimension to his refusal that Homer does not explain?
I believe that Agamemnon is so embittered by the long siege that he has begun to question whether the sacrifice of his daughter, Iphigenia, was worth it. In his mind, if he can't have his daughter back, then no one gets their daughter back.
Homer never mentions the sacrifice of Iphigenia, so this insight into Agamemnon's motivation never makes it into the Iliad, but it provides a bit of logic to what is otherwise an illogical act.