It's my understanding that the issue of income inequality comes from stagnating wages for a specific portion of the population. In the past, all wages for all skill sets, would rise (periodically) to meet inflation. Somewhere along the line that stopped for those in middle and low income brackets. Their wages stayed the same, despite continued inflation.
The high income brackets, however, continued to see wage increases, sometimes well above what they would need to account for inflation. Obviously successful people shouldn't be punished for being successful, but when a CEO gets a huge bonus, and none of their other employees do, it creates the kind of negative image that spurs a debate on income inequality.
This is also fueled by the decrease in the value of education. More prospective employees have bachelor's degrees than ever before. Which means highly educated people are fighting it out for low paying jobs. And employers have no choice but to ask for higher and higher levels of education in order to thin the hiring pool.
So it's no longer true that a highly skilled person will get paid what they're worth. Rather, the only way to avoid the low and middle income brackets is to be born into a rich family. Obviously it's still possible for anyone to become rich, but the pathways have narrowed and the middle earners are forced to work paycheck to paycheck.