Income inequality creates social tensions in two directions. From the point of view of the majority, it isn't just a question of envy, although that's real; it's also the distortion in prices of important assets like houses in good school districts.
And from the point of view of the extremely affluent, it becomes all too easy to disengage from the rest of America and to see one's wealth as divine reward for special genius, rather than for many other factors, including blind luck. That sense of difference in turn leads to the absurd sort of narcissism and insensitivity to others.