If you have a major flood in your garden you don't rush to sort out a dripping tap. First you tackle the flood then you investigate the tap. Anyone shouting 'the tap, the tap!' would be quite rightfully lambasted as unhelpful.
Nursing & childcare are statistically women-only due to sexism against women, not due to sexism against men. These are low-paying, low-power jobs where only the bosses tend to be male.
If some women are protectionist about men joining their ranks (which, by the way, I highly doubt until I see some evidence — I have met many of both) it is probably due either due to fears of pedophilia (almost certainly unfair) or due to fears that men will be promoted over them (very real).
Anti-male sexism in the work-place is a red-herring. It is a minuscule problem compared to anti-female sexism and, to my ears, carping on about it sounds as misplaced as white males going on about being discriminated by ethnic minorities.