I tend to think that the real problem isn't income inequality, but rather, perceived opportunity upward mobility.
It's depressing to hear people claim "that guy is too rich", in a society that has relatively (compared to other nations) few barriers to self-improvement.
The problem is that the important decisions, the things that shape you, are already made by the time you;re old enough to own them for yourself...... Stay in school.... Don't do drugs... Don't commit crime... Value family... build positive, constructive relationships and peer groups..... Don't have children you aren't ready to raise to a life you would envy for them... By the time a kid turns 10, it's nearly impossible to break free from the cycle unless they've been blessed with strong guidance. Unless they've learned the value of hard work and are capable of delayed gratification.
If you're hopeless when you're 12, how do you break the cycle?
"Income equality" would be a rally cry for anyone stuck in that place.