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I observe it

Americans give more to charity than any other society. How is that greed?

Those are humans acting out of a natural desire to help others. Unfortunately, in Euro-American culture, those "charities" are simply multinational corporations who have obtained government-approved "tax-free" status, and siphon all that "charity" to a few individuals.

"The entirety of Euro-American society is based on greed".. Society is the cultural norms, the institutions, the government, not the humans involved. There are many humans living within the sphere of influence of that society who do act for the good of others, but the simple fact is that's not what is most valued & rewarded by the society. When the definition of "success" is fame, fortune, and power, then clearly greed is the underpinning of the society.

I don't think most Americans define success that way. We do aim as high we can, in terms of socioeconomic status. I think it's important to have high aspirations, while staying humble and content. A difficult balance, indeed.

And we definitely respect those who do good. On the flip side, some people only do good to assuage their own egos.

The cultural definition of success is wealth, fame, positions of power though. People want to get autographs from actors & sports players, Billionaires are considered successful, no matter how they got those billions, Senators are looked up to rather than seen as public servants, etc. Again, culture & society do not necessarily refer to all humans living inside their bubble, but that is what "America" is about. The corporation known as the United States itself is dedicated to monopoly of currency, military conquest, and consolidation & expansion of its power over humans.

The people express their culture by their behavior, don't they?

There are materialistic people, such as you describe, but I don't see that they are a majority. If anything, a country should be identified with the majority of people who are essentially kind.

Human behavior is made up of a variety of factors, of which culture is one.

The fact that humans are all naturally kind (except sociopaths), doesn't change the fact that this culture and economic system reward greed, that every "citizen" is actively funding mass murder, kidnapping, extortion, and oppression, or that people considered "successful" are those who accumulate "wealth", have power over others, etc.

Success from Oxford Dictionary:

  1. The accomplishment of an aim or purpose.
    1.1 The attainment of fame, wealth, or social status.
    1.2 A person or thing that achieves desired aims or attains fame, wealth, etc.