You are confused because you are looking at the stated ideals of this country and not the actual practice.
America was built and designed to be a country that primarily existed for the landed white male gentry. Even other men couldn't vote for the first 100 years, and the whole system was a very carefully calculated pyramid of power and privilege. Not surprising, since that was pretty much all that our dear founders saw all around them as examples. Just as "religious liberty" was shorthand for "our brand of religious intolerance - just not the one we left behind" rejecting the power of a king and a other hereditary royalty did not signal a belief in actual equality (despite some of the nods in that direction). It simply meant the right to create and maintain our own dominance based hierarchy. There is not and has never been much of a meritocracy happening, what with nepotism, the good ole boy network, to say nothing of all sorts of laws that up until about 60 years ago kept a lot of people from even having the legal ability to compete. The fact that people are willing to try to overthrow the government to try and return to that time ought to tell you something about how deeply rooted it is in our culture.
The fact that these restrictions no longer take place in law doesn't mean they have evaporated. Of course, we've made some progress, but the hierarchy is very much still in place, as evidence by the amount of egregious racism that still takes place, to say nothing of all the ways that women are still hazed and harassed to try to get them out of male-dominated professions, and the way that they are often undermined and discounted when they stay. Just read the newspaper - this stuff is happening egregiously on a really regular basis still. This is what sexual harassment is about as well - trying to remind women that they are sex objects and not the competition. The fact that this is no longer happening uniformly does not detract from the pervasive cultural dynamics - because that's not how social science works.
As I made clear in the story on the different types of hierarchy, there's nothing wrong with stratification - that is based in merit, and operates by power to or power with. Unearned cast systems based primarily on immutable traits which are maintained by power over are dysfunctional and inherently problematic.
I recommend that you check out the website of the renowned systems scientist, Riane Eisler, called The Center for Partnership Systems for more detailed information and resources.
