The absolute quality of people's lives is of great importance (and is tracked in such measures as life expectancy and some global poverty stats), but inequality is a serious problem because of power[1]. Gross inequality of wealth directly leads to gross inequality of power, and that is (axiomatically) assumed to be bad because it means that the outcomes of many people's lives are directed by the few who have power over them.

[1]: https://en.wikipedia.org/wiki/Power_(social_and_political)