Absolutely correct, Jack
The big assumption is that women actually want to do all the jobs men do and the only reason they aren't is that there is a great big conspiracy to hold them down. 
For decades our schools and universities have been trying to get more women into STEM programs, but, through free choice, fewer women than men take these courses. 
As for the wage gap, time and time again statistical studies that look at both the level of education and the field of education, experience, and hours work show only a miniscule difference between men and women in earnings.  
Even in highly regulated fields, such as family physicians,  women tend to earn less than men because they put in fewer hours.  Clearly, more women than men make the reasonable choice to forgo longer hours at work for more time with family or other leisure pursuits.  Of course, this is changing as it is now acceptable for men to also put in fewer hours at work to spend more time with their kids.