That's part of the title of a Slate post by Matthew Yglesias (he probably didn't choose the title). The rest of it is "America is Leaning Out."
It's fun to parse those kinds of titles. This one uses both a link to Sheryl Sandberg's Lean-In movement and a type of exaggeration: "fewer and fewer women are entering the labor force." The doubling of "fewer" implies continuous diminution. The Sheryl Sandberg linkage implies that the women "choose" not to be in the labor force, in a manner opposite to "choosing" to do well in one's career or job.
But the research the post discusses has nothing to do with either of these suggestions.
It has to do with the rates of labor market entry and exit after an earlier recession and after the most recent one, and tells us nothing about continuous diminution of women's labor market participation rates or the reasons for the figures the researchers found.
The authors of that study use two tables to argue that it's reduced labor market entry by women in the lowest age categories which is the major cause of the falling labor market participation rate in the US. I reproduce the second table here. It shows entry rates by age groups and separately for men and women:
The caption at the bottom of the table must be wrong. It applies to the first table in the research paper, about labor market exit. The proper caption should probably be "the percentage of people in labor force who were not in it four months earlier."
The crucial data, for the purposes of the post's title, has to do with what is going on in the younger age groups (up to age 54, even). Women's entry into labor force after the most recent recession is lower than after the 2002-2003 recession, while men's entry in the younger age categories is slightly higher or the same as in 2002-2003.
This is all the data tells us, by the way. It doesn't tell us what caused those differences. To discuss them is speculation, ranging from the possibility that women are more likely to choose education at younger ages than men (thus leaving the labor force temporarily or delaying their first entry) to the possibility that women are "choosing" to stay at home with their children while men are "choosing" to enter the labor force.
The comments to the Yglesias post have the usual MRAs telling us that women naturally prefer to stay at home and that at least this gives the poor unemployed men a better chance to fulfill their god-given male role and so on. But if the reason is that women choose more education, the MRAs could tell us that women are hogging all the good spots in colleges and so on. They are a gift that keeps on giving. And yes, I know I should not read comments.
It's worth pointing out that the study (which is not given in much detail in the pdf I linked to) is a comparison of the aftermath of two recessions. It's not about the general labor market participation rates of women and men in general. In that sense the information it conveys is much more limited and cannot be used for the kind of emotional arguments the title suggests.
Because the debate abstracts away from that contest it fails to ask what might be different between the 2002-2003 recession and the most recent one. For example, could it be the case that female dominated occupations are simply not hiring as much after the most recent one, compared to the earlier one? And if that is the case (say, because of the belt-tightening of health care and education industries), could it not be the case that women are more likely to find their job search fruitless and therefore more likely not to try entry or re-entry into the labor force?
I don't know the answer to that. But focusing only on the supply side of labor is probably insufficient. The demand side matters, too, and women and men are still largely working in different types of jobs and industries.