"Statistics that show the women earn $.80 for every dollar a man earns. However, these statistics only account for median income for all earners. When we normalize for variables like levels of education, number of hours worked, age and workplace/field, we find that the wage gap is reduced to virtually zero. After these adjustments, we find that women are making less because they more often choose field like education over engineering. Women also work less hours on average, take time off to have children and other activities that amount to time away from the workplace. These choices are what account for these differences. They are not systematic forces but rather the choice of women."
This is the argument that I agree with, because it is solid and based on evidence. There are very few cases where actual wage discrimination has occurred, and the companies have had legal repercussions because wage discrimination based on sex has been illegal for over fifty years. Additionally, companies would make more by hiring more women if it were the case that they could simply pay them less. This isn't the case, and you can see that by simply seeing that men make up most of the work force.
The reason that they say "virtually zero" is because they can't take into account every single variable. They can only say that, within a margin of error, sexism is not present.
And a research study on this exact topic can be found here.
This isn't a link to a study but rather an analysis of the studies that says within itself that the wage gap cannot measure the effects of discrimination because of all of the factors not being taken into account. There has never been a study that showed discrimination on any wider societal level that wasn't easily countered by proper analysis or another study.
Much of my response is drawn from the Economic Policy Institute. Their work can be found here.
This is a link to a calculator which only takes two factors into account. This is useless to countering any of the points you were trying to counter, because not all of the needed variables were taken into account. Women still chose lower-paying jobs and take more time off to raise their families in the form of more flexible hours and maternity leave.
I'm skeptical of any argument that concludes a specific population chooses their inequalities.
They do because male and female brains are different. This causes men and women to choose different careers, and women to take more time off to raise their families.
"We also know that women earn less than men in every state and region of the country, and that once you factor in race, the pay gap for women of color is even larger."
People of different races also choose different jobs (same reference from above). This is because Asian people have better education and set-up for higher paying jobs than whites, while Hispanic and black people have worse education. (I know, generalizations because the data we're working with is based on averages.)
It seems that you have read the anti-fem argument and not quite understood it yet. None of these studies have taken into account the variables needed to show that actual sexism is the only remaining cause for the gap. There is no evidence for any sexism apart from the few and far between court cases that have been brought up. This is because people are paid based on job performance rather than sex.
If you can provide any study that is comprehensive and takes into account:
and still shows a gap, then that would mean that more women should be suing for higher pay. But right now, no study of that sort exists and real life shows that women are suing very infrequently and are not favored in overall hiring because companies would be able to pay them less for equal work.