The short answer, @_Whitetigress, is that the American Dream is about “not accepting” being stuck in any way: not stuck educationally, status-wise, career- or income-wise or stuck in one’s outlook for one’s own children and family. These days, for example, gays are not accepting their status as second-class citizens by virtue of their sexuality. Good on ‘em!
Yes, people anywhere can be hard done by. And if they understand and accept the premise of the American Dream (as millions have, and perhaps millions more do not), then they “do not accept” that they, their families and others like them will have to remain where they are in perpetuity.
It’s not a guarantee of success, by any means. That’s why it is “a dream”. It’s not always the American Reality, unfortunately.