In the first place, to frame the issue as income inequality is to lump together different issues that are not especially related. What we call “inequality” is caused by two different constellations of problems.
At the top end, there is the growing wealth of the top 5 percent of workers. This is linked to things like perverse compensation schemes on Wall Street, assortative mating (highly educated people are more likely to marry each other and pass down their advantages to their children) and the superstar effect (in an Internet economy, a few superstars in each industry can reap global gains while the average performers cannot).
At the bottom end, there is a growing class of people stuck on the margins, generation after generation. This is caused by high dropout rates, the disappearance of low-skill jobs, breakdown in family structures and so on.
If you have a primitive zero-sum mentality then you assume growing affluence for the rich must somehow be causing the immobility of the poor, but, in reality, the two sets of problems are different, and it does no good to lump them together and call them “inequality.”