Conservatives have longed decried the corruption of the word "equality". "It used to mean equality of opportunity", they say, "and now it means equality of result." I would add to that. It used to mean equality of opportunity, equality of responsibility, procedural equality, an equal right to plead one's case. It meant an equal right to ask for things, not an absolute right to get them. It did not mean equality of result or equality of starting conditions.
It's hard to say where a longing for equality came from. What I sense, when I look at a psychological need for old-fashioned equality, is a profound resemblance to the longing for autonomy. A community of completely autonomous individuals would be hard or impossible to create, but it's easy to conceive.
What jumps out at us when we visualize a community of completely autonomous people? Total equality, in the old-fashioned sense. If you're annoyed by your neighbors, chafing under the serfdom imposed by feudal overlord, burdened by taxes, whatever, you feel the root of that desire for autonomy. Then reality returns and you see that a person who needs firewood, food, shoes, and health care cannot live on his own because no one can create the skills and capital need to simultaneously be a lumberjack, farmer, baker, butcher, shoemaker, and physician. Whether or not it is The Way the World Should Be, absolute autonomy is only a dream.
Yet as with any dream we carry something with us back into the waking world. Perhaps the classical liberal's idea of equality is a nod to the dream.
Thus, I believe there is even more separating the old-fashioned idea of equality from the corrupted leftist idea. They don't have the same psychological root. Classical liberals wanted autonomy and settled for equality. Leftist resentment is close to the opposite of autonomy. Leftists want to punish those more diligent, responsible, and talented than themselves. They stole the term "equality" to use as a weapon against their betters.