Income Inequality is a euphemism for the politics of envy, which always lead to "redistribution", which in turn is a eumphemism for property theft.
Inequality is the natural state of the world, and even tyranny can't change that. Tyrants and their elite bureaucracies are seldom the equals of those they subjugate. Mao didn't starve to death along with millions of his people; and the greatest concentration of wealth in America today is in the sixty mile radius surrounding Washington D.C., the very enclave of people who are creating the inequality that they condemn. We choose to have equal rights, but we will never have equal ability or motivation, and these are reflected in unequal life outcomes.