Use the symbolism of different characters and places [West Egg, East egg.. Etc] to discuss who or what really killed Gatsby.
Part of what makes Fitzgerald's work so "great" is how it operates on so many symbolic levels. In deconstructing the Jazz Age, Fitzgerald gives a glimpse of an aspect intrinsic to modernity. There is no sole agent of action when it comes to human suffering. For example, in Greek tragedy, the audience is able to identify a particular person who is responsible. While there can be discussion and deconstruction, blame and responsibility falls on one person's shoulders. Oedipus is guilty of unspeakable acts, Creon punishes Antigone, Medea kills her children. There can be discussion and analysis of other forces responsible, but we can fully ascertain as the audience who is the agent for human unhappiness
Modernity gives more complexity, greater options, but little in way of absolute truth. Fitzgerald paints this picture when Gatsby dies. On face value, George Wilson shoots him. Believing that Gatsby is the man who ran over Myrtle, George takes action and shoots Gatsby. However, Gatsby's death can be seen as the symbolic fault of many. Fitzgerald does not let many really escape without blood on their hands. Places and people bear symbolic responsibility for what happened to Gatsby, reflecting a certain sadness and universality in Gatsby's suffering.
In terms of characters, I would suggest that the Buchanans have to be seen as bearing responsibility for Gatsby's" death. Daisy is literally responsible for Myrtle's death and in her cowardice for Gatsby to take the blame, she becomes morally responsible for his. Her lack of courage is the reason why George believes he is killing his wife's killer, believing that he is striking a blow against the hollow and uncaring wealthy. Tom would have to bear responsibility for Gatsby's death, as well. He steers George towards Gatsby, clearly suggesting that Gatsby is responsible for Myrtle's death. George's anger is intensified by how Tom is carrying on with Myrtle, contributing to his already eroded condition. When Tom describes George as "a blonde, spiritless man, anemic, and faintly handsome," it is clear that his withered state is because of Tom's savagely cruely attitude. Additionally, Tom evades responsibility from any of his actions, refusing to acknowledge his role in the lives he has wrecked. Fitzgerald describes both husband and wife as responsible for so much and yet finding ways to simply cause more damage to more people:
They were careless people, Tom and Daisy- they smashed up things and creatures and then retreated back into their money or their vase carelessness or whatever it was that kept them together, and let other people clean up the mess they had made.
Fitzgerald asserts that the socio- economic realities that govern the worlds of East Egg and West Egg is a reason for Gatsby's death. The hollowness of wealth that exists in both worlds makes things and objects more valuable than human emotions. People like Jordan Baker and Klipsringer move from party to party, and parasitically live off of those who are foolish enough to believe that something sincere and authentic lives within them. The socio- economic reality that governs both worlds is one in which there is nothing else but a symbolic "valley of ashes." The lifestyle and social construction of both Eggs, where new money seeks to become old and old money simply mocks at anything that is not them, is responsible for Gatsby's death because no one represents an agent of transformation in a world where things are more important than people. Fitzgerald's indictment of the worlds of East and West Egg and the people in them help to explain why there can be symbolic blame parceled out to many in the novel.