Why does Achilles reconcile with Agamemnon?

Achilles has suffered horribly, but he is still hotheaded and impatient. He is interested in revenge, and anything else is a waste of time. In contrast, Agamemnon spends a great deal of time making elaborate excuses. His speech opens with a nervous entreaty that a speaking man should be listened to, and he works hard to lay blame for his dishonorable treatment of Achilles on previous madness. He knows that his own troops in great part blame him for the disasters that have befallen their army. The gods, he says, blinded him. Achilles has no patience for the ceremonious giving of gifts; he is no longer interested in having Agamemnon restore his honor to him. Odysseus and Agamemnon both desire to have the rupture between the men formally healed, but Achilles' main interest is Hector's death. He shirks the social activity of eating with his companions, and he impatiently bears the ritualized apologies of Agamemnon.