Inequality in all its forms is not bad per se. Economic inequality is bad because (1) on a moral level, it is grotesque that some people have so much while others struggle immensely (and we can do something about it - money can be transferred, looks cannot), and (2) money amplifies the political voice of those who have it, undermining the concept of democracy - especially when they use that voice to direct benefits of the political system to themselves, at the further expense of the have-nots. Socialism for the rich and capitalism for everyone else, as the saying goes.

Plus, the sheer magnitude of inequality is immense in the area of wealth. It follows an exponential distribution; those other things you mentioned follow a normal distribution.