Respect and disrespect are major themes in Homer's Iliad. The reason for Achilles' wrath is due to the disrespect shown to him by Agamemnon in Iliad I. When Agamemnon forces Achilles to hand over to him his war prize, the slave girl Briseis, Agamemnon dishonors Achilles in front of the entire Greek army.
Because Achilles has been dishonored, he decides to withdraw from the fighting. Furthermore, he removes his army from the war as well. He appeals to his divine mother Thetis to help restore his honor, which she does with Zeus' help. Later, in Iliad 9, Agamemnon tries to repair the broken relationship with Achilles by offering him all manner of fabulous prizes to return to the fighting. Achilles, however, refuses.
Only after the Trojan Hector kills Achilles' friend Patroclus does Achilles return to the fighting and mend his relationship with Agamemnon. When Achilles kills Hector, it is Hector whose corpse is treated with disrespect as Achilles uses his chariot to drag the dead warrior's body around the plains of Troy.
Ultimately, at the end of the epic, honor/respect is restored to both Achilles and Hector, as Hector's father Priam comes to the Greek camp and buys back his son's body from Achilles so that Hector can be given a proper burial. Priam convinces Achilles to turn over the body by appealing to him as a father and reminding Achilles of his own father:
"His words had moved Achilles to tears at the thought of his own father, and taking the old man’s hands he set him gently from him, while both were lost in memory. Priam remembered man-killing Hector, and wept aloud, at Achilles’ feet, while Achilles wept for his father Peleus and for Patroclus once more, and the sound of their lament filled the hut" (A.S. Kline translation).