You have a number of issues with your narrative. "Quit the profession or go part time in order to raise kids". So what other reasons do women have for quitting the profession, other than because men are too victimized to be stay at home dads?

-- edit: fwiw, I googled stats. According to the American Association of Medical Colleges, 2017 was the first year ever that female medical school enrollment was greater than male medical school enrollment. I also went to graduation by year as far back as 2002, and it has always been more men than women. So yeah, your statistics are bullshit. Care to offer a source? --

And mind you, being a stay at home parent is considered a low-prestige, low-pay role. To the extent that it's discouraged for men, that's a result of a sexism that puts men in a dominant role and demeans them for doing "women's work".

The idea that men aren't teachers because the media paints them as sex-crazed is absurd. The gender disproportion of teachers existed long before the media mentioned such things at all. And you offer no evidence whatsoever for the assertion.