What are Menelaus and Agamemnon fighting about after the war in Book 3?
Agamemnon was the son of King Atreus and Queen Aerope of Mycenae and was considered the leader, or commander-in-chief, of the Greeks during the Trojan War. Menelaus was his younger brother, and he was married to Helen of Troy, who was the supposed cause of the war, being the most beautiful woman in the world.
In book 3 of Homer's epic poem, The Odyssey, the answer to the question of what Agamemnon and Menelaus are fighting about can be found in lines 102-147. In this section, Nestor is responding to the plea of Telemachus to tell him information about his father, Odysseus, whom Telemachus assumes has died. Nestor speaks highly of Odysseus and his cleverness in battle, and then recounts the sacking of King Priam's citadel.
Nestor goes on to describe the trouble that they had after this. He says that some of the men acted unjustly, and stirred the wrath of the gods. He describes the quarrel between the brothers Agamemnon and Menelaus as one that was instigated by Athena, who was angry with the men for their behavior. The quarrel between the brothers was about their next moves. Menelaus wanted to return over the open sea, but Agamemnon wanted to wait and offer sacrifices to Athena. The argument escalated to harsh words and stirred up all the men's anger until most were fighting. They end up separating, each following his own ideas, and neither brother's actions please Athena, which sets them up for further hardships along their journey. Below is a quote from Book 3 which contains Nestor's explanation of the quarrel:
Zeus planned a grievous journey for the Argives, because some had behaved incautiously and unjustly. Many came to a dark fate, through the fierce anger of the bright-eyed goddess, daughter of a mighty father, stirring a quarrel between Atreus' two sons. Hastily and informally, they called the Achaeans to an assembly at sunset, and because of it the sons of Achaea arrived sodden with wine. Then they spoke, and explained why they had gathered the host. Menelaus suggested they made their return over the wide sea the priority, but this displeased Agamemnon, who wished to delay them there, and to offer holy sacrifice to appease Athena’s deadly anger, not knowing foolishly that she would not listen, since the will of the everlasting gods cannot be swiftly altered. So the two of them stood there, exchanging harsh words, until the bronze-greaved Achaeans, divided in opinion, broke up in almighty uproar.
The quarrel that occurs between Agamemnon and Menelaus, two brothers who led the victorious Greeks in the Trojan War, was instigated by Athena, who was angry at the Greeks in the aftermath of the conflict. Menelaus advocates immediately returning, though the Greeks are drunk with celebration, but Agamemnon wants to wait to offer sacrifices to Athena. According to the poem, the two "stood bandying hard words," and the men divided in their allegiances. About half left immediately with Menelaus, about half stayed with Agamemnon. The latter made his way fairly quickly home, where he was murdered by Aegisthus, a usurper who took his wife Clytemnestra, and the former spent some time trying to return, actually getting blown off course for Egypt on his way back home. So neither man was fortunate enough to experience the favor of the gods after the war. We learn all this from Nestor, who tells Telemachus, the son of Odysseus, the whole story when he visits him on the way home. Significantly, Odysseus remained with Agamemnon to perform sacrifices to Athena.
According to Nestor, in Book 3 of the Odyssey, Athena stirs up the quarrel between the two brothers, Menelaus and Agamemnon. “Athena set them feuding, Atreus’ two sons” (Book 3:153) Her anger at the Greeks stems from an incident before the fall of Troy. A Greek warrior tries to rape Cassandra, King Priam’s daughter, who is hiding in a temple of Athena’s. When the Greeks do not punish this misdeed, Athena dooms them to a long, difficult journey home from Troy.
The brother’s first disagree about the best way to set sail for home. Menelaus argues that the ships should leave without delay; Agamemnon counsels that the troops first should offer sacrifices to appease Athena’s wrath. The goddess provokes their argument to the point that it fuels a fight between the ranks of soldiers who follow each brother.
At dawn, the men following Menelaus sail away while the men following Agamemnon hold back, camped on the beach. Neither plan pleases Athena. She will make sure that both sides suffer hardships and misfortunes along the way.