When discussing inequality an important distinction is between equality of outcomes and equality of opportunities. Everybody is (or at least claims to be) for the latter whereas opinions on the former sharply differ on the left and right.
I always liked to clearly distinguish between these two concepts and often argued that we should strive for more equality of opportunities, i.e. cut the welfare state in order to make kindergarten and tertiary education free ... until evidence convinced me that you cannot neatly seperate the two issues:
