Final answer:
Achilles re-enters the battle of the Trojan War to avenge the death of his friend Patroclus, who was killed while wearing Achilles' special armor. The loss deeply affects Achilles, pushing him to put aside his personal grievances and seek retribution against Hector, the Trojan prince responsible for Patroclus' death.
Step-by-step explanation:
Achilles, the famed Greek hero of the Trojan War, is prompted to re-enter the battle due to a deeply personal and tragic event. Initially, Achilles withdraws from the combat out of indignation when Agamemnon takes Briseis, his prize of honor, claiming disrespect to his prestige. However, a pivotal moment that incites Achilles' return involves the death of his beloved comrade and cousin, Patroclus. Patroclus dons Achilles' special armor, crafted by the god Hephaestus, to rally the Greeks who are faltering in battle. In this armor, he is mistaken for Achilles and is slain by Hector, the Trojan prince. The loss of Patroclus pushes Achilles beyond his grievances, and he rejoins the war with a fiery resolve to avenge his friend's death, an act that is fated to lead him to his own mortal end, vulnerable only at his Achilles heel.