Describe, in your own words, the squabble between Achilles and Agamemnon, and feel free to bring out whatever elements that personally interest you the most. Thank you.

The conflict between Achilles and Agamemnon is the driving force behind events in the Iliad. In the first book, the Achaeans have recently sacked a small city and taken, as prizes, two women, Chryseis (who goes to Agamemnon) and Briseis (who goes to Achilles). A plague infects the Achaean camp shortly thereafter, and Achilles suggests the army consult a soothsayer to determine the cause of the plague. The soothsayer states that Apollo has sent the plague to punish Agamemnon for taking Chryseis and that the plague will not dissipate until she is returned to her father. Agamemnon is angry that he has to give up his prize and seems to feel that Achilles has set him up somehow by consulting the soothsayer. He agrees to send Chryseis back to her father but demands that Achilles give him his prize, the girl Briseis, as recompense.

Achilles is insulted because he is not to blame for the plague and, consequently, does not deserve to lose his prize. He and Agamemnon get into an argument, the thrust of which is that Agamemnon is the "High King" and is demanding obedience from Achilles. Achilles counters that Agamemnon is not his king, and he does not, in fact, owe him any loyalty. The exchange gets so heated that Achilles draws his sword to kill Agamemnon, but the goddess Athena stays his hand. Achilles decides to wound Agamemnon by withdrawing his troops—and himself—from the battlefield. Everything that happens in the poem follows directly from this decision.

The thing at stake in the initial squabble is not, in fact, the spoils of war (Chryseis and Briseis), but rather personal honor. Agamemnon is resentful that he is "to blame" for the plague and that he has to give up his prize to end it; he shifts that resentment from its rightful object (the father of Chryseis) to Achilles, who is, in turn, angered that he is being punished when he has not done anything wrong. Because honor is at stake, neither man is willing to de-escalate the argument—Agamemnon attempts to throw his weight around and demand Achilles' loyalty to him since he is the commander of the Achaean troops; Achilles informs him that he is here voluntarily and is happy to pack up and go home if Agamemnon does not back off.

This argument is a neat framing of the cause of the Trojan War. The men are essentially fighting over women that they see as prizes: who has earned the women, who gets to keep them, who has to give them up. The women are proxies for the men's personal honor, and therefore giving them up (or having them taken away, as Agamemnon threatens to take Briseis) is a tremendous blow to one's pride. It is incumbent upon both men to restore their sense of honour somehow, which is why the argument escalates so rapidly into a fight. This parallels the Trojan War itself, whose root cause is the abduction of Helen, the wife of Menelaus. The Achaeans are only waging war on Troy to avenge the honour of Menelaus and get his wife back for him. When the poem opens, the Achaeans have been fighting for nine years, and what might have been resolved quickly by simple diplomacy, has turned into a grinding war because neither side will accept any loss of honour by turning the woman-prize over.