Isn't it just an objective fact that men are more intelligent and competitive and therefore intellectually superior?

What studies have you run to support this supposed "objective fact," sweetie?  What studies have you even read?

I notice you don't provide links to any.

Not very "intelligent" of you, dear.

Too funny.

If thats the case (and I presume that you are a guy) then why are you on here asking a question? You should be telling us all how it is, alpha male. Instead you are sending questions out into the ether.  Seems like youve undermined your own argument. 

"Isn't it just an objective fact that men are more intelligent and competitive and therefore intellectually superior?"

Men's behavior are at the extremes whereas women's behavior is in the middle.  So you will always see men overly represented as leaders, geniuses, guru's, prophets and so on.  But then you will always see men overly represented as criminals, thugs and buffoons.  Women are comfortably in the middle, in general, as a group.

This is why you are getting answers that both fully support, and fully deny your assertion.  Because strangely ... they are both true dependent on any individual person's group of men they know and/or deal with.
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The main reason why women are behind men in the work place, is 'babies'.  If a woman decides not to combine motherhood with a career/not have children, then there is no reason why she isn't able to become a CEO, President, Leader of the United Nations.

Having children, stalls a parents career, whether they are female or male.  It takes longer to crawl up that ladder, if you've taken 15 - 20 years off.

Men haven't proved that they are superior in any form.  More wars have been started by men's ineptitude at negotiation.

No, research shows women make better leaders and have done much for Society but history books left out information on women who contributed in big ways as well as small ways which impacted society.

You're equating becoming a CEO as being correlated with intelligence? Studies have shown that there's a greater correlation with narcissism and psychopathic tendencies. So the answer to your question is no.

The biggest idiots I've known in my life have been men. So my answer is no.

No that’s not objective.  “ Contributions” to society is too vague to mean anything. Would war-mongers contribute to society? Do poets contribute?  Do those who don’t procreate contribute? Do jazz musicians contribute?  How about those who spread propaganda? We each see things differently and I have no idea what makes a person superior to another. 

Bless your hearts, all of you. Women who love you let you believe that.

Female might be smarter than male between the elementary school to high school age. However, after the college age, male will start succeeding female overall.

Ideologies are educated female don’t need to be so smart.
Ideologies are educated female need to get married at the certain age.
Ideologies are educated a woman marry to a good man better than succeeding in the job career.
Ideologies are educated a woman to take care of the husband and family.

However, In China, there is a place called Shangerila, the Yunna provinces in Southwest of China. There is a group of minority are female lead minority. 

But you know what, in a female lead society, those men are piece of garbage to us because ideologies educated men need to be strong, so men take more responsibilities to support the family financially, and men used to suffer more stress than women.

We are all live under ideologies. Ideologies educated us how should we react, how we think, how we view matters, and how we judge matters. These ideologies are invented by the philosophers, psychologist, and sociologists. Philosophers usually work in a churches, schools, or government as a purist, professor, or politician. 

Doctors, social workers, sometime can be a philosophers,too when they become an expert in Philosophy, Sociology, Psychology, and History. When we judge what is good or bad, right or wrong, all based on these 4 principles.

When we convince ourselves that male and female with the different responsibilities to the society, that might make you feel better. 
If you keep judging everything, you will never feel happy.