The Iliad is about the feud between Achilles and Agamemnon, a feud that occurs during the Trojan War. Book III of the Iliad has nothing to do with Achilles, a little to do with Agamemnon, and everything to do with why the whole war is happening at all.
Note added August 19, 2024: The war is happening because Paris is God’s gift to women. By his own account, he is excellent in the “gifts of peace,” and these are “as little to be scorn’d, / As to be wonne with strength, wealth, state …” It is good to recognize that some things cannot be obtained by “strength” or force. Achilles recognizes this in Book I when he refrains from killing Agamemnon. However, Paris scorns not only strength, but also wealth and state. I suppose it is “state” that lets Hector and Agamemnon come to an agreement about a duel between Paris and Menelaus that will end the war. Paris breaks the agreement by running away to visit the prize of his excellence, namely Helen. Homer has Venus spirit Paris away, but I take this to be a poetic embellishment, agreeing with Eva Brann in Homeric Moments: Clues to Delight in Reading the Odyssey and the Iliad (Paul Dry Books, 2002; pages 41–3):
But the gods’ face-off effects nothing; at least nothing happens that could not happen without them. And so it is always; Zeus himself disclaims responsibility for human fate right at the beginning of the Odyssey …
To be sure, as I said above, nothing is ever done that could not have been done by the humans themselves …
Polytropy 