Anyone who can't see the problem with extreme income inequality is extremely short-sighted, and has no understanding of history. In fact, one of the very things that allowed the United States to emerge as it did was BECAUSE it was at least a relatively more equal society than most others at the time of it's beginnings, and that's true for several societies that have become relatively "successful" in the modern world, and the reasons for that are incredibly obvious. Look at what has happened in the societies where income is most skewed, just look at the history of Latin America and it's extremely easy to see- a small minority owned nearly all the land, all the resources and all the capital. Such a ridiculously wealthy minority has no need to utilize all the resources in their optimal way, and the inequality has been very hard to eliminate. The national economy begins to stagnate, because the domestic market begins to shrink. Political freedom diminishes, because anyone can face the reality, that the richer you are, the more influence you will have. That small percentage of the population with vast resources can easily monopolize information, and thus monopolize power. They begin to be above the law, even. Government spending begins to slant strongly towards the interests that are controlling the information (and political power).
Sure, "Never in America!". Well, obvously it's not entirely like that now, but the thing with income inequality is that it can very easily spread. It takes two homeless people to produce several homeless children, and considering the fact that if the major interests that fund government campaigns have no need for public education, then education goes down. The underclass grows. In any relatively serious economic situation more join the underclass and not as many come out, all the while it becomes increasingly easier for the already very wealthy to keep expanding their wealth. All of it happening over the course of the years, obviously, not a sudden impact. But it's quite dangerous, and it could very well happen.
Just to bring back the point of all this, the justice of income inequality rest on the necessity of a free country and only works within one. The socialism verses capitalism debate has been over for some time. (Communism does not look good, even on paper!) One need only observe North and South Korea and have a half a brain. Europe is moving to the right and the more they do, the better off they become. (see: East Europe and Ireland) 
Who made up that rule ?
