"Human beings have no fixed characteristics and outlook, eternally permanent...In capitalist society there is the most extreme disintegration of social responsibility: the system makes “every man for himself” the main principle of life. The outlook of people can be changed by changing their material conditions, the way in which they get their living." (Emile Burns, "Introduction to Marxism", 1957, International Publishers)
"The fact is that the individualistic every-man-for himself-and-the-devil-take-the-hindmost behavior of most human beings in capitalist countries is not part of our biological heritage.
It is the result of our conditioning in a society dominated by the motive for private profit. Eliminate this driving motive, and a different kind of behavior develops, one that seeks the personal good in the common good." ( A.B. Magil's "Socialism: What's In It For You", 1946, New Century Publishers)
"Does it require deep intuition to comprehend that man’s ideas, views, and conception, in one word, man’s consciousness, changes with every change in the conditions of his material existence, in his social relations and in his social life?" (Marx & Engels, "Communist Manifesto")

Greed is not an inborn human trait, it is a learned reaction to the system of society that is imposed on us. Change the system, change the behavior. NOTE: no one is saying that this change would happen overnight, or even in one or two generations. But the reaction of humans to protect each other and their society under great duress shows that we are a communal species, our instinct is for cooperation and for sharing. Only one sector of society preys on our misery, profits from our misfortunes, makes a religion of profit and greed. They are called capitalists and there isn't any rule that we have to keep them.