Who is responsible for causing the deaths in the Iliad, Achilles or Agamemnon?
First, the Iliad is a poem about the Trojan War. In this poem, Menelaus and the Greeks have declared war on Troy with the avowed purpose of obtaining back Helen, wife of Menelaus, who had been abducted by Paris. In this war, all of the soldiers on the Greek side are trying to kill Trojans, and the Trojan soldiers are trying to kill the Greek soldiers. That is what happens during wars; soldiers try to kill each other.
In the conflict between Agamemnon and Achilles over the war prizes, both are equally culpable. From a modern perspective, of course, seizing young women from their families, enslaving them, and raping them is morally wrong and thus both men are acting in a way we now would consider grossly immoral. From an ancient Greek perspective, both men were concerned about their honor and maintaining face.
Agamemnon failed to demonstrate good leadership but Achilles also failed to act as a team player, letting his pride get in the way of his duty of obedience and his loyalty. Thus the actions of both men ultimately harmed the Greek cause.