Earlier quoted context omitted.
I’m not sure what anyone was promised, but just from a basic logical perspective, if opportunities are really equal then, over time, outcomes will equalize as well. I’m not a progressive, but if over decades of pursuing liberal policies outcomes are not equalizing, it seems to make sense to try to figure out why and find something better to try.
I think liberalism cares about liberty not equality. Pure equality is not possible while people have parents.
The argument that your parents make you not equal is exactly what liberalism is trying to reject. Someone should not be treated differently based on their heritage (monarchies anyone?).
In fact, since you believe you can't be equal due to parentage, you probably agree with some of what progressives have to say. The current system isn't equal.