Unless you personally know the other person, I'm not quite sure how you make these claims. On the face of it, you're slinging mud at walls and, of course, some may stick. In other words, your claims may be on point
some of the time.
Some Yale students (undergraduate or graduate) may have had literate, educated parents. Mine aren't. Many others here could say similar things.
Some Yale students may have come from Andover, Loomis Chaffee, and the like. Not all. And I'm willing to bet there are numerous students who came from high schools like the ones you describe. Or, as in at least a few cases, came from "schools" that were essentially converted sheds or barns.
Some Yale students may not have had to worry about taking care of their families or being the breadwinner during adolescence. But others did.
Some Yale students may not have lived in shady areas. Many did.
We're an intelligent lot, certainly. And certainly there are many others who are much more intelligent than us. But Yale does not exist to serve the world. Yale is not a public service. Yale is exclusive by design. You don't get here by being intelligent, but by the same token, being here does not mean we're more intelligent than you (in the plural sense). The fifteen year funnel notion that the other person described is, in fact, much more a filter of ability, grit, and exceptional achievement than you could ever dream of. A minority of students here come from the sort of Gatsby-ish background that popular myth suggests. There are students here who may not be the most intelligent in the world (certainly, not all of us are MENSA members), but they are, for the most part, people who have proved time and again their exceptional qualities. There is a reason this institution has been an incubator for leaders around the world.
Yale is not a meritocracy. Yale is one among a few institutions that have carefully cultivated the ability to choose from an exceptional pool of human beings each year. If you point out the issue of legacy admits, I'd ask: why not? Why not give back to those who have given to Yale? I don't simply mean monetary contributions, though certainly I would wish to signal appreciation of someone who has endowed a chair, a library, or has done something to grow Yale as an institution. But, in general, if someone has reflected well on Yale, then I believe it is worth nurturing that relationship. So, yes, not all legacy admits are evil.
The world is not equal, and equality is not a given. We will never be equal, as long as scarcity exists. But instead of whining about how "all Yale students are privileged" and thereby exposing your own prejudices and jaundiced perceptions, why not make the best of your circumstances, much as we have of ours?