Are you suggesting that women are naturally smarter than men? No, as far as intelligence goes we both have very similar capacities. There are plenty of dumb men and smart women, and plenty of dumb women and smart men. Equality will not be unbalanced by a more intelligent gender because neither is more intelligent than the other.
I am not suggesting that either gender is the smarter, but due to brain lateralisation and the different capacities for various tasks held by those with male-type or female-type brains (incidentally, both types of brains are found in either gender) make the two brain-types good for very different tasks. And the types of tasks that are becoming more common as the human race evolves and society develops are favoured by the female brain, tasks like writing, conversation, political lobby and diplomacy are becoming far more vital to Eudaimonia than, say, mechanical engineering and professional soldiering.
Moreover, in the west especially, the education system favours the female brain, part of the reason girls consistently out-perform boys on school tests is because girls respond far better to the teaching-styles found in American and European schools.
Scientists are now beginning to realise that what the Psychologists have been telling them for years, that Gender is not black and white, that it is a spectrum, may not be quite as silly as they first thought. I may well be male in appearance, but my lungs may well lack a Y chromosome. Different parts of the body often exhibit different gender phenotypes, and more recent studies have found that the ratio of male to female DNA in our bodies has a significant impact on the 'boyishness' or 'girlishness' of our personalities. A builder, for example, might be 60% male to 40% female, genetically speaking, whereas a make-up artist might be the opposite.