The question is, why do people do as the system rewards? Why do they strenuously seek out rewards to be gained in any system, to such an extent that they'll change their apparent nature to do it? That sounds like greed to me. The fact that capitalism sets up the reward structure so that if you're really greedy one of the best ways to succeed is make something people really want, or something that increases efficiency, it's a really useful coincidence.
Also, you say humans have been the same for a 100,000 years, which seems to indicate that there is a human nature, and that society hasn't really changed them. Isn't that the opposite of your earlier point? It certainly supports the capitalist point, if you actually examine how people acted in history. Especially if you look at what happens to systems of government and economics that rely on people being altruistic and not greedy (the Church, communism, monarchy to an extent).
Also, I'd like to point out that in any society, but especially in a humanist, free society where being altruistic is a choice and not something forced upon you, there is always a reward for being altruistic, whether it's internal conscience assuaging, or extrnal favor-gaining. Furthermore, it is completely possible to be greedy in the persuits of gaining money, and then altruistic later: the whole point of getting money is not to have it, but to use it they way you want to use it. That can include charity.