One of the reasons men don't enter fields like teaching and nursing is because they pay poorly.  It's a chicken-and-egg question:  which came first - the low pay or the predominance of women?  Either way, I think a man in, say, construction, probably earns more than a teacher, and certainly begins earning sooner.

I think the second claim is most likely true for nursing.  Not everybody can be a doctor and yet for demographic and economic reasons, health care has been one of the most consistently expanding industries.  It will be a place that people of both genders will go to for jobs, from nurses to home health aides to back office and marketing functions in those fields. I'm less sure about teaching, reliant as it is on public funding in an era of ill-planned austerity.

I seem to remember reading about some migration from heavily male construction injuries to the health care sector during the financial crisis.

Teaching has deep cultural roots as a job for women. Prior to any organized education systems, women were tasked with teaching their children. As the nation progressed Normal schools where teachers were trained were almost entirely women, as that was an acceptable job for a woman. There were men in Normal schools as well, but it was one way for women to continue their education.  It wasn't always acceptable to educate women. In fact when my grandmother graduated from high school in 1925, her father who was from Ireland said, girls don't go to college. However, her  mother who was from Norway, said, Papa, Betty is going to the University of Washington and he finally said ok. But he was not convinced it was good for her or for society. And she did not go to the education college, she was in the school of journalism and then moved to Oregon on her own to write for a newspaper. 

It is completely cultural the lines society has drawn on what men do and what women do, which is why those fields that men often populate pay greater salaries. And women from the beginning of time, iff they happened to be in a position that men mostly did, were always paid less for their work. Always. We still haven't made our way over that bar just yet, although we are getting closer. 

But it is undeniable that there continue to be cultural norms that affect women and men and the jobs they do.  It is true that being a male nurse must come with some side eye from other men, who harass men who they see as less tough than they are, and anyone who does a woman's job is less tough than they are, and this is one of the many ways our culture has impacted career choices.  By the same token I have met many a woman who seem to believe only men can do certain jobs, like my job. I'm a data analyst, data admin, programmer type, and just recently I'd done a big analysis for the Ballet, it spanned decades and the women upstairs in Development asked if the young man in our office produced the analysis. I was pissed and I ranted about it, oh and still am. Those are women in the Development office, not men.  Ugh and in my former position at a college I was harassed by the Dean of Enrollment services who used to tell me daily that I didn't look like a nerd at all, whatever the fuck that means and then he would ask me weekly to move in with him. This is all cultural and has nothing to do with what people can or cannot do and what their skills may or may not be because of their gender. I happen to be a damn solid programmer/analyst even being a woman. I retrain constantly to pick up new languages, the latest being python, and I live in Seattle, where being a programmer/data professional is the norm and where many women do the same job I do, and yet, even being here, and Seattle is incredibly progressive, even here we experience those weird culturally embedded women's work/ men's work beliefs. I am constantly shocked by this. 

As to the nature of the article, first of all efforts should continue to be made to expand our culturally embedded gender limitations. One way to achieve this of course is to continue our efforts to educate women/girls that they too can be scientists and engineers.  However, we should also continue to encourage men to become teachers and nurses because if men feel like they can make an impact on society through those professions they should absolutely do so, in the end it impacts those students we are educating in those fields that is it acceptable culturally. And then maybe we become more gender neutral as a culture, which would be a great relief and make our nation a better place.