I believe true equality is a high ideal much like world peace in that neither will ever happen. I don't say this to be a pessimist but as student of human behavior.
The goal of most people is not to be "equal" but instead be considered "special". We want to "stand out" be better than average!
If our educational system in the U.S. decided to do away with our grading system consisting of A,B,C,D, F and simply went with a P (for passed) and F (for failed) a lot of folks would be highly upset! Someone who got 100% would get the same grade as someone who got 65% correct; a (P). Imagine playing a game without keeping score and at the end everyone goes home with a trophy.
Human beings are competitive. They have a need to (compare) themselves to their peers. Everyone wants the perks that come along with being "the best" or a "VIP", first class travel, 5 Star Hotels & Restaurants, tailor made suits, exotic vacations, the big house on the hill or ocean front property. Most of all they want respect.
One's peers who see you as their equal will not have the same respect as those who envy your position. The clerk VS the executive.
Words like (mediocrity and parity) which mean equal are frowned upon. Everyone wants to be "above average". We want to stand out, not be the same. I suppose if anything we want an equal opportunity at becoming "special".
Most people want to be "admired" or "respected" because there is something "exceptional" about them. This is what fuels our ambitions.
Individual traits both physical and mental along with personality will always cause some people to be viewed as better than most.