About the whole men v women intelligence thing.
Men are more genetically diverse than women, meaning there are more outliers in both directions.There are many studies showing this.
Some studies have concluded that there is larger variability in male scores compared to female scores, which results in more males than females in the top and bottom of the IQ distribution.
It's why there are more men in special education, and more male chessmasters or top-of-the-class males.
On average there probably isn't much of a difference between intellectual
ability, but it's arguable that women have less incentive to be intelligent and thus are on average not as intelligent. Not sure about this as more women now go to college than men, but on the other hand STEM subjects are male dominated. Anecdotal, but many girls I talk to here do something like event management, or child care, or even fashion studies. Which I deem to be less mentally stimulating as engineering (my class was 15 to 1 male to female).
This brings me to my last point, intelligence is somewhat subjective. Most people seem to define it by something that they are personally good at. So I have an engineering mind and consider problem solving to be of utmost importance when it comes to intelligence. But I'm shitty with people skills, people with good people skills will probably argue that they are more intelligent as people skills are more important. Etc.
This is why it can be hard to have the men v women argument. Women will define intelligence based more on what women are good at, men will define intelligence more on what men are good at. So we could actually both be right, just with different definitions of intelligence.