Power and honor divide Achilles and Agamemnon because both men feel that they are not given their due respect from the other.
Homer shows power and honor in a distinctive way. In the Classical society that Homer describes, both are external. For example, power is shown through outward displays and honor is depicted when an individual deferentially concedes it to the other.
This construction underscores the relationship between Agamemnon and Achilles. Agamemnon believes that Achilles is not showing honor towards him. It is for this reason he establishes his power over the warrior with his claim on Briseis. Doing so is a way for him to display his status. For his part, Achilles does not feel that Agamemnon shows respect to warriors. Achilles believes that Agamemnon does not merit respect because he does not sacrifice on the battle field as a soldier or warrior does. Achilles believes this to be dishonorable because the king takes that for which he has not labored. Recognizing that the only power Achilles has over the king resides in his fighting, he withdraws from battle. This significantly weakens Agamemnon's desire to claim Troy as his own. Achilles' withdrawal is a power play to maintain his integrity. This reality helps to explain the division that takes place between both men.