I wonder where the author of this opinion piece have her numbers from regarding womens' wages. I've looked a little into the issue, and I certainly don't recognize them. Here is what I've found (notice that there are sources at the end of the comment).
When we look at absolute numbers, women earn 44% less than men, and when we take other variables (like number of hours worked, years of experience) into consideration, women earn 21% less than men[1]. Other research has shown that there is "only" a 12% wage gap that can't be explained by differences in work patterns etc.[2]
No matter if the wage gap is 12% or 21%, it is not acceptable that people who do the same work gets paid different wages.
Also, while a part of the wage difference can be explained through differences in working hours, work experience and occupations, it doesn't mean that these differences aren't caused by discrimination and stereotypical gender roles.
This can be expressed in several ways:
Stereotyping of occupations:
A number of professions are considered men-only, or more suited for me. Some because of the physical work involved some because of a perceived mental difference between men and women. An example of the later, is science in general, where some people claim that men have a better aptitude for understanding it. Some of these people, like Lawrence Summers in the past, are in positions where they make decisions on hiring and promoting people.
Different perception of work done by men and women:
Study after study has shown that both men and women have a tendency to evaluate men as better than women, when everything else is equal[3]. This means that men will get better results (and promotions) for the same work.
Men are also perceived as better leaders than women, since they "take charge", contrary to women who "take care"[4]. This will lead to promotion of men over women, even if they are considered equally qualified on basis of their past work.
Gender patterns in society:
The overwhelming pattern of US families is to consider women as caregivers and men as earners, even when both work. This means that if they decide that one of them should reduce their working hours, it will in most cases be the woman who does so.
From a pure economical perspective, it also makes sense, since women earn less than men for the same hours, so the relative cost of reducing the hours is less for the woman than for the man.
Penalizing of part-time workers:
People who work part-time earn 17% less than people that work full-time[5]. Since women are more likely to work part time than men (25% vs. 11% [6]), women are more likely to be penalized.
Women are also more like to be paid by the hour than men (63% of all female employees vs. 58% of all male). I am unsure how this affects the pay level though.
So all in all, on top of the explicit gender-specific discrimination of women when it comes to pay, there are a number of other issues that also leads to discrimination of women, which leads to lower wages for female employees.