I think some men stay away from this work, in part, because it’s often low paid, undervalued labor. There is a long history of women’s work being undervalued, especially in terms of pay. At a recent talk with a woman who works on these issues (she’s a dean at a business school), she pointed out that while HR used to be well-respected and have good pay, the numbers of completely reversed in part because women now dominate the field (you could argue with her about causation, etc, but there is something going on).
Men are not being kept out because they are men, but because they are acting non-gender conforming (by wanting to care for children - something that has a long history of being women’s work). I think it’s a bit absurd that because men are being kept out of low paying, socially undervalued work, they are victimized the same way that women are within a sexist society. I agree that men suffer under the patriarchal structure too, but it really isn’t the same as to how women are treated. It’s just not. And if we do address issues women face, I’d imagine that the men who are victimized will see an improvement in their treatment, too.