Income Inequality - Bad or Good?

I read an interesting article from the Federal Reserve of Saint Louis. The author Thomas Garrett speaks about income inequality less as a bad thing but more as a by-product of a well functioning and healthy capitalist system. The income level of an individual, he says, is a measure of their productivity. Today, though, people only think that the wealthy are wealthy because they have a lot of money.

Garrett argues that there should be a distinguishing of income inequality and poverty, and that the latter should be the only one that should receive policy-based reform. In summary, we should not hurt the wealthy, yet we should encourage those in the poverty brackets to receive more opportunity to become more productive.

Sounds good to me and made me more open to income inequality but I don't know how reasonable he is, because how do you give aid to one side of the society without taking from someone else?