What Makes a Wo/Man?

I've been listening to discussions on masculinity and responsibility in the context of fatherhood in the black community. And it strikes me that what is being identified as emblematic of mature masculinity is not gendered in anyway that I can see.
Responsibility is an often repeated key word: parental responsibility, social and sexual responsibility, fiscal responsibility. Even among those who have a hierarchical view of gendered relationships there is no suggestion that women should not be parentally, socially, sexually or fiscally responsible. So then, how are those forms of responsibility masculine?
Granted, there are those who say that women should not have to support their children financially or parent alone. But the single mothers who successfully parent their children - even when they are referred to as mother and father - are generally not stigmatized as less than feminine.
Are there characteristics of a well adjusted adult that are gendered?
On as essential level, I have always believed that women are born and made (with a nod to Simone de Bouvoir). We are socially shaped by our families of origin and the culture in which we live. That shaping is based on the implications of our bodies in our cultures.
People who are born with a particular genital configurations (or variations based on it) are categorized as female. People who live like (socially constructed) people who are identified as female are themselves identified as [trans] female without regard to their genital configuration.
So, some of us are identified as female by our bodies and the world at large. Others self-identify and are affirmed by some of the world at large. But in neither community have I heard a definition of woman (or even female) that is ubiquitous to the gender or distinguishable from man or male.