That article seems to have an assumption that men do not want to look after their children? That is one of the weirdest things that transitional masculinity says tbh. Loads of men are very close to their children and soppy as anything!
One thing I did read, which is weird, men who have primary care/ look after small kids a lot, have a measurable reduction in testosterone. Which is amazing really, as a mechanism presumably to make him calmer etc when looking after kids which can be very annoying and frustrating! So I suppose they have a point, if you want your men to be angry, violent, unemotional "men's men" then you probably don't want to give them babies to look after, but, what about the mental health thing? I thought party of it was about feeling detached, wouldn't this help?
I also liked that the article said women weren't oppressed by men but by "nature". Don't know about you lot but I have had a lot of grief from owls and harvest mice 
(I think she means it's natural for men to oppress women, as the ones who have babies it makes sense that we are "weak" and men should control us).