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.
The constitution of the US (a liberal system) contains this phrase you might be familiar with. "All men are created equal". Equality is a central tenet of liberalism.
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.