Even the paper you linked to doesn't claim that equality CAUSES unhappiness. A correlation might exist, but some of the authors' suggestions include:

if happiness is assessed relative to outcomes for one’s reference group, then greater equality may have led more women to compare their outcomes to those of the men around them. In turn, women might find their relative position lower than when their reference group included only women.

or

simply a change in how women answer the question.

(i.e. it's more socially acceptable to claim unhappiness)