There have been a lot of political talk on "disparity" and "equality" lately in US. The underlying assumption often is that equality is necessarily good, and that most people would benefit from the reduction of disparity.
However, it is well known that enforcing equality usually leads to the reduction of the quality of life for the majority of people. More often than not the equal wage in the equalized society is much less than the median wage in a mildly unequal society. There have been enough historical examples of that.
And yet, even confronted with readily available historical evidence of the side effects of equalization, most proponents would still prefer equalized society. That raises a question: what is the underlying motivation of the desire for equality? Is it derived from the desire for the better life, despite the evidence to the contrary, or is it derived from envy, the desire that the Joneses wouldn't have more?
I'd like to make a clarification, prompted by the answers by @virmaior and @Niel de Beaudrap. This is to do whether equality has a value in itself, isolated from other considerations.
Imagine the society of 10 people, 4 of them have $10 each, 3 of them have $20 each, 2 of them have $40 each, and 1 has $120. Suppose they voted for the "equality law": everybody should have the same amount of money, but executed it by making those who have more than $10 burn the excess amount rather than distributing all the cash equally. From the point of view of equality alone the society has progressed: now everyone has $10 and GINI is a perfect line. Nobody benefited financially, in fact 60% majority lost.
However, there could be a certain emotional "benefit" in the above scenario for the poor 40%, and perhaps for the "lower middle class" 30% (who actually lost half of their savings): there are no more "rich" people whom the poor ones perceive as looking down at them. No more wealthy ones to attract the females desired by the poor, etc. The desire for such emotional benefit that comes with lowering the rich ones to one's own status has a word in English language, and the word is "envy".
If you think that redistribution of wealth would be more like combining all the wealth into a single pot and dividing it equally then think again. It is always easier to raze a building that to build one. If a law would pass that all buildings in a town must be of the same height that would result in removal of upper floors of taller buildings, not in mounting more floors on top of smaller buildings. In fact, the tallest building may get completely demolished.
There have been a few examples in History where an attempt of equalization resulted in the destruction and/or lowering of the upper classes with no financial benefits to the lower ones. Translating the above example to the realities of, say, Communist Russia would be "execute the top 10%, send the next 20% to Gulag, and reduce everybody else's wealth to $8". That is, even the "poor" ones loose financially (although relatively mildly). The only benefit Russians ever had was the fulfillment of their yearning for "social justice", which was driven mostly by envy.
"Equality of opportunity" is usually achieved in a similar way, by reduction of excessive opportunity rather than any improvement. If the law would pass in the USA that all public schools must provide the same educational experience, and private schools would be eliminated, that would result in all schools being equally bad, thus providing all kids with the same (lack of) opportunity. Things wouldn't improve anywhere, but the "equality of opportunity" would be achieved.