What is the hypernym for man and woman? I don't think it is gender because that would've been male and female.
You might be looking for "gender identity". Male and female are genders, but a person can identify as a man or a woman regardless of whether they are physically male or female.
But of course, this is a very fuzzy subject, and if you ask 10 different people you're going to get 15 different answers.
Man and woman are gender. Social roles defined by society. There is nothing genetic or biological about wearing high-heels, for example. Men don't do that (usually...) because social norms say they shouldn't.
Male and female, on the other hand, are a biological matter of sex that have nothing to do with social norms. With apologies to Simone de Beauvoir, you are born female but society makes you a woman.
Honestly, it might be easier (and possibly more correct) to switch the hypernyms in your example.
Male/female makes a bit more sense with "sexes" as the hypernym, since it is talking about physical gender characteristics. This sort of debate shows up in the comments about Barrie England's answer. In that case, man/woman would have the hypernym of "gender", since it is a more socially constructed division.
Of course, they are close enough in meaning you might get away with using either interchangeably if you're using them casually - either male/female or man/woman , or else 'sexes' or 'genders'. But if you want to talk about these sets of terms or distinguish between them, the standard usage is that "sexes" go with male/female for denoting the physical, and "genders" go with man/woman for social meaning and construction.
"Male" and "female" refers to the property of belonging to a particular category in a categorization scheme, and/or those categories themselves. "Man" and "woman" refers to an individual with that property, along with several others, most notably being human and being of a certain age and/or state of maturity.
If you get hypernyms by removing distinctions, then the hypernym is whatever the word is for something possessing all the remaining properties. "Human", "person", "individual", "adult" and "member of a (two-)gendered species" are all reasonable choices, depending on which categories are relevant in whatever context you want to use such a hypernym.