You, as an individual, may not care. Unfortunately, historical evidence and social science evidence suggests that (bearing in mind that you as an individual may not care) when income inequality grows too great, other parts of society begin to suffer and eventually break down. This even affects things like the average health outcomes for the people living in the unequal the society.

There's a strong correlation that indicates that poorer health outcomes, higher crime, poorer standard of living all go hand in hand with greater income inequality.

Again, you may not care, for your own sake, but the country is a fair bit larger than you, and this problem does affect us all, whether we care or not.