Men outperform women in competitive contests even when no physical effort is involved. Men dominate chess, poker and competitive computer programming.
Well, the examples you offer do not require social skills. What I'm proposing is that men will probably still dominate the programming field, but women will increasing own and manage the companies the programmers work for. Being a CEO is essentially a political job that requires social savvy, not something chess players, poker players and programmers are well known for.
Women will, on average generally speaking, out perform men in the social arena because they've had to develop such skills over thousands of years to compete with men's physical advantage. Social skills are becoming ever more important in an increasingly urbanized inter-connected society, and physical advantage is rapidly becoming irrelevant.
Today's men retain the advantage of centuries of discrimination in their favor, but as you've surely noticed, that advantage is quickly fading. When men and women are able to compete fairly in today's environment, and even more so as we move forward, the women will on average have the advantage.
Summary: Women are smarter than men, because they've long had to be.