I think the concept of "everybody should be treated equally" works best if we held all social institutions to that standard and not just the state and large corporations.
I am not a luck egalitarian but I think they make a good case for why everybody isn't "treated equally" in nominally liberal-"democratic" societies. People inherit inequalities, and if we are serious about holding people to their choices and having results depend solely on their choices, then much needs to be done to eliminate this inherited inequality.
But of course, that is not very popular. So institutions do the next best thing, they try to make-up for their inherited inequalities by giving extra opportunities to those who did not inherit favorably with the consideration that "inheritance x same choices" can give different results, if the first product is different.
The right-wing extols this inheritance because they believe that certain groups are superior to others. The actual left-wing aims to reduce these inheritances either directly or eliminate their impact on consequential inequalities. The center tries to balance the two, aiming for whichever policies are least objectionable.
