A lot of people who attack mainstream economics will say it assumes that people are always greedy, and that this isn't the case, therefore it is based upon false premises. I feel like this is unfair - I wouldn't describe "economists believe everyone is always greedy" as a strawman, but it's an unfair way of putting it.
Economists tend to assume people are self-interested. I'm not certain how to cash out the difference between being "greedy" and being "self-interested", but I'm fairly certain there is one. For example, I would much rather eat a nice meal than be poked in the eye. Given a choice between the two, I would choose the meal. I don't think that makes me greedy, but it is definitely a self-interested choice.
Perhaps we might say that being "greedy" implies a certain lack of concern for others. There are people who I care about deeply, and I would say that their well-being contributes to my well-being. Hence, if I had to option to provide a benefit to my brother at minimal material or temporal cost to myself, I would be likely to provide this benefit. We can conceive of this as being self-interested, but it seems weird to describe it as greedy.
Alternatively, perhaps we think of greed as being overly concerned with material wealth, as compared to other valuable things. If someone were to pave over a beautiful garden in order to build houses, I can imagine them being described as a "greedy developer".
In any case, I don't think either of these words - at least as used in the most conventional sense - is really an appropriate way of describing the way economists conceive of self-interest. It's true that our models frequently exclude charitable spending and gifts to other agents, but if you want to call failing to give to charity greedy then (while I agree with you) you're going to have a hard time arguing that people aren't basically greedy, given the rather small size of charitable donations. (And also given that Effective Altruism is seen as radical and unusual. Since I heard of it, EA has always seemed rather obviously correct - at least, so long as one accepts moral realism - and yet, EA evangelism is not just a matter of explaining the basic ideas to people, you generally have to convince them over weeks and months. This strongly suggests to me that, when people donate to charity, the extent to which they help people is not generally at the forefront of their mind.)
Perhaps the best way of explaining the way most people understand the word "greedy" is that it should be viewed as relative to a socially agreed baseline. So it's "greedy" not to pay taxes, and moreover, "paying one's taxes" is defined relative to the intent rather than the letter of the law. (This "intent" can be very nebulous, of course - what is one person's "incentive to promote valuable business and job creation" is another person's "corporate loophole"). But since most people don't really give to charity, it's not greedy not to give - just so long as you do give when everyone is doing so (e.g. school non-uniform day, a leaving present for someone at the office, icebucket challenge).
This is not to say that the assumption that people act "rationally" in the economist's sense is entirely warranted: merely that to suggest it has too low a picture of humans is quite the wrong way to go about attacking it. A far better attack - one which, in my view, has a lot of truth to it - is that it overestimates people. People do not generally set out purposefully so as to best achieve their goals. Indeed, they make certain consistent and predictable errors. This is indeed something of a challenge to the axioms of neoclassical economics - although, with a better awareness of human psychology, it may well be possible to repair the faulty assumptions to make better predictions.