I've heard from many people that America offers full ride scholarships for bachelors students, with enough money that they don't have to put any money from their side. However, such a possibility does not exist for masters.
Why is this?
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Many universities in the US are funded by the States. New York State has a substantial number of such places, both research and teaching universities as well as some designated colleges. Their mission is, in (large) part, the general education of the state's citizens, with the idea that it will lead to economic growth.
The US also has a very economically diversified population, from the incredibly poor to the incredibly rich.
To match these two things, state universities, at least, often provide funding for individuals, though it is now less (compared to need) than in the past. As noted in comments, this "funding" is really just providing the education (tuition) at low cost, possibly zero, leaving living and some educational expenses to individuals. Books, for example, are typically very expensive. Residential colleges may not fund room and board.
And "full ride", whatever that means, is probably restricted to residents of the state with rare exceptions. (See personal note below)
And, my impression is that states, in general, are getting "stingier" about funding education in general. The federal government doesn't provide much funding other than grants for research, leaving the general education to the states. And there is a large difference between states as to willingness to provide funding.
Private colleges and universities also provide scholarships to undergraduates, in the form of low or zero tuition cost, so as to try to attract the best students, which, long term, increases the reputation of the institution.
However, at graduate levels, the education is seen (rightly or wrongly) as more of an individual responsibility. If you want it, you gotta pay for it. This is probably the explanation you want for the master's level. The doctoral level is a bit different, since doctoral students, especially TAs also contribute to the (important) undergraduate mission as well as freeing research faculty to be more productive. So funding is there at that level.
Masters students, however, having less to contribute and more to gain are sort of "on their own". But, it is also true that you don't need a masters to join a doctoral program, so, compared to some other places, there are fewer "masters only" students than might be otherwise expected. Many (most?) of those are destined for jobs outside academia, which can be higher paying, seeming to lessen the cost burden long term. Modern trends seem to question that assessment, however, with too many students having unsustainable debt on graduation from both bachelors and masters programs.
And, field is also an issue. STEM fields are currently better funded and with better job projects than things like, for example Philosophy and History (etc.) that are (IMO) indispensable to an educated populace, but now comparatively poorly funded. There are even proposals in at least one state to do away with such programs focusing too much (IMO, again) on the purely economic value of an education.
Caveat: This may be an "old guy" view. I earned my doctorate just over half a century ago. Long ago, at a good private college I got a great education at zero cost with a grant for tuition (partly state funded) as well as a campus job that, together, paid all my bills after the first year. I doubt that would be possible today. That was truly "full ride", though I contributed my labor.
Some people and governments believe that education is a human right, and provide a free education paid for by the government accordingly.
In the US, there is national free public education up to age 18/"grade 12".
When a university provides "full ride" scholarship funding, they are often doing so because they see their mission as extending the right to availability of education to the post-secondary level. Because there is not really government funding for this mission in the US, it is necessary for schools to charge most students tuition, but they can also give reduced or even completely free tuition to students who are seen as most in need or most deserving (or, often a combination). An alternative "selfish" reason is that schools are in competition with each other for reputation, and attracting some of the very best students through financial incentives may raise the reputation of the school. I'll add that here I am answering what the typical reason would be for offering a bachelor's degree scholarship; it should not be mistaken that these offers are themselves typical: almost every student in the US pays tuition, though they may take loans to pay later.
For the most part, a masters degree in the US is a terminal degree that allows someone to earn a higher salary than they would otherwise, so there's more of an expectation that masters students will treat it like an investment in their own earnings, and pay out of those future earnings.