Nature abhors imbalance.
She does not require "equality" necessarily, but she will demand equilibrium. A tree whose roots are not deep enough will blow over in a storm. An enormous boulder may perch precariously on a much smaller base, only so long as that base doesn't crumble. A dam will hold water back until the water finds the smallest crack to start its breakout.
That same Nature exists in us. We call our innate need to find balance "justice", and although we may not always understand how to best achieve it, I think we all, for the most part, know justice when we see it.
One of the best rules, the most simple of rules, is what many of us know as the "Golden Rule". I don't think there has been a culture that hasn't come up with their own particular, eloquent wording to express the same simple idea that lives in every human heart.
If we could all just follow this rule, every day, in everything we do and with everyone we meet, what a wonderful world this would be.
Act only in ways that I wish others to act towards me.