This argument is actually dealt with by Marx himself in the Manifesto, where he puts forward his view that there is no such thing as fixed “human nature.” Human attitudes and behavior are constantly reshaped by the changing economic systems in which people find themselves. Engels went on to spend a good deal of effort showing that early hunter-gatherer and village societies depended far more on cooperation than on competition.
The Russian anarchist Peter Kropotkin made the classic argument against social Darwinism in his Mutual Aid (1902), and leftist social scientists have developed it further. In many cultures prestige or authority are more highly prized than property, and competition may be expressed by acts of even radical “selflessness” such as giving away almost all one’s wealth in the “potlatches” of certain northwest tribes of Native Americans. Capitalism, socialists argue, simply brings these otherwise marginal emotions to the center and exaggerates them, stripping people of the strong ties which unite groups based on tradition, honor, religion, etc.
This is an argument that cannot be settled. No large socialist or Communist state ever managed to create a population of ideal Communist citizens–though it is worth noting that many contemporary Russians voice regret for the disappearance of old patterns of cooperation in the new capitalist era and are decidedly ambivalent about the virtues of competition.
Communists may have sounded naive when they foretold the creation of the new “socialist man,” but anti-Communists sounded equally naive when they asserted that contemporary attitudes toward property, work and money were universal truths unchanged throughout history. It was not entirely implausible to argue that if Europeans could change from believing in the divine right of kings, the necessity of permanent feudal ties, and submission to the Church, they could change further to reject individual self-interest, competition and private property as eternal truths which predominate in society.