If the worth of people is incommensurable, not comparable, then they cannot be unequal because an inequality cannot actually be defined. Thus, they would not be equal or unequal but existing in a state of uncertain equality. That is, if we define that equality is a mathematical term, so too is inequality. And to define two things as existing in either of the two states requires the ability to measure them for comparison.
You are trying to shift the burden of proof. I make no universal claims about the relative worth of human beings. A person who claims that they are all equal is making a positive claim and as such must provide evidence for that position, which would be impossible as they cannot even provide a coherent definition of equality much less provide evidence for it.
Not only is equality a positive claim, the believers is this mystical idea demand action be taken as a result of their faith - action which is often quite radical and/or violent.
Given that, you argue that inequality is a social good, because if people rejected the belief that they were equal to other people, they would naturally be content with their lot in life. Leaving aside the question of whether the ability to be discontented is potentially a good thing or not for the moment, this conflicts with your statements about the uncertainty of measuring inequality. What stops people, even ones who believe in inequality, from saying "I am better than person X with things Y and Z, I deserve things Y and Z more than they do"? That is, what reason is there to believe that people can both be utterly bamboozled by notions of equality and yet simultaneously would recognize their natural superiors on sight?
I've made no claim that inequality is a social good, only that the misbegotten belief in equality is a social bad, as any widespread belief in mistruth tends to be.
Any claim of superiority would have to be justified as would be the supposed benefits such a superior person claims to deserve. If people get paid $20 for every widget that they make and person A makes 20 widgets a day and person B makes 10 widgets a day, then person A could justifiably claim to be the superior widget maker and that they are entitled to $400 for a day of widget making while person B only gets $200 a day for making widgets. If person B's claim that they are equal to person A and therefore are entitled to make as much money for a day of constructing widgets as person A, then that is a belief that is seemingly (assuming no important information has been left out) unjustified.
Finally, going back to the ability to be discontented, surely that is itself a social good if the inequalities are unjust? That is, as you have laid things out, it seems that you might agree with "people in the USSR ought to have been contented with the fact that Party membership sped you up in the waiting line to get a TV, or that members of the PolitBuro had access to the best dachas, because assuredly they deserved them more because they had them". Is that accurate? I must confess I don't really see why it would be inaccurate.
I don't think that contentment is necessarily good nor do I believe that discontent is necessarily bad. Content or discontent should be appropriate to the situation. The desire for equality, often in practice meaning sameness or at least selective sameness, isn't a justifiable reason for discontent. For example, if you own a home which you are happy with, that is a size that fits you and your family well, and you feel contented with that home; would it not be inappropriate to become discontent, and in fact hostile, upon discovery of someone else with a larger house?
As Teddy Roosevelt said "Comparison is the thief of joy."
A hungry person should strive to acquire food, a slave should strive to acquire freedom, the lonely should strive to find friendship and/or companionship. None of this is contingent on what food, freedoms, or friends someone else might have.
If we return to relations between the sexes, a feminist woman might demand equality. She might say that men make more money than women, just as an example. Since equality has no meaning, it is an irrational idea, she substitutes sameness for equality. She demands that women make the same amount of money, on average as men. Of course, this is selective sameness, she wants women to make the same amount of money as men on average but doesn't seem to care that well over 90% of job related deaths are men, that men work harder jobs, with longer hours, with fewer fringe benefits. Those extra male dollars, like the simplified example of widget makers above, are earned and not merely given. So instead of merely focusing on what accomplishments might bring her contentment, she instead selectively chooses certain advantages that men have while conveniently ignoring men's many disadvantages and then cries for equality.
We would be far happier, and actually more moral, if we simply rejected the idea of equality and realized that all people have a multitude of strengths and weaknesses and also a multitude of advantages and disadvantages and seek to fulfill our wants and needs rather than feel victimized because all outcomes aren't the same for all people or groups of people.
