I'm coming from an Islamic perspective, which some may view as oldschool. Just a heads up.
Masculinity and Femininity are defined in Islam, however that doesn't imply that they are direct opposites. Some will tell you femininity is about weakness and masculinity is about strength (bullpoop, if that's the case then why do we always happily mention Sumayya bint Khayyat as the first female martyr who died in battle and how the prophet pbuh would hug and kiss children even when their own fathers would not?). There is a contextualized 'strength' and 'weakness' in both men and women. We do see the roles as complementary and not interchangeable. For instance, the role of the mother, due to the physical sacrifices a woman must make is seen as a beautiful and very much respected role. I fear that nowadays people associate respecting motherhood with being uneducated and perpetually pregnant in the kitchen. Not at all - it is incumbent upon all Muslims to be educated. We do believe that in general (Islam directly addresses the general picture and later scholars discussed the exceptions), mothers have a closer connection to children than fathers. We do think it is the role of the father to protect and provide for his family. That does not mean women cannot, nor does it mean that men must be overbearing and overprotective, but we do believe men are more physically equipped for protective roles.
As a female I don't feel the least bit hindered by these different attitudes toward femininity and masculinity. There is no excuse for father absent homes, and that has usually been much more of a social problem than mothers who abandon their families. I've read from several sources that fathers are fundamental to childhood development. Does this mean all nuclear families do better than alternatives? No, like I said, Islam acknowledges the big picture and leaves it up to us to determine what to do in exceptions.
When I get a husband he must take after the prophet pbuh and be a good role model for children. The prophets' first wife took care of him for several years, (she was a wealthy businesswoman and he was a poor merchant), so a stay at home dad is not out of the question. However he must be willing to protect me and stay committed for the duration of our marriage (which hopefully will last a lifetime).