Newton, interestingly enough, died in Middlesex--an apt transition into why it appears that a binary approach to gender is insufficient in general.
I’ve lately been trying to define the difference between the genders (beyond just chromosomes or genitalia) and it’s really, really hard to say that “All men are ____” or “All women are _____.” Statistically, you can make arguments (brain size, approach to problem-solving, tendencies to listen or sympathize or interrupt, etc) about the differences between genders, but I can’t think of any characteristic that is fundamental to either masculinity or femininity. There are always some men or women who don’t have a certain trait stereotypical for their gender but who are still very much men or women. It gets confusing because we, as laypeople, sometimes use 'gender' synonymously with one's physical sex and other times we mean something like personality types.
I’ve asked a few friends if they can think of any characteristic that all men must have or that all women must have in order to be a man or a woman. So far, we haven’t come up with anything. By all means, if you can think of anything that every woman does (nurture? listen well?) or every man does (be aggressive? provide for a family financially?), I’d love to hear your thoughts. Suffice it to say, though, that when you get down to it, the two categories of man and woman can’t really be defined beyond “I know it when I see it” except, again, perhaps statistically. A stay-at-home dad who is 5’4’’ without much body hair or muscle mass can still have a deep bass voice and be a wonderful father to his children. And someone who is tall, muscular, and aggressive can be no less a woman than a demure home-schooling mother of nine.
This is why I feel like binary gender theory is incomplete. It is an impossible-to-fully-define shorthand into which we shoehorn the people we meet. And that fundamental flaw is apparent even before we get into the hard cases. For example, what do we make of gay people? Is a man who is attracted to men less of a man? I don’t think so. Further still, what of hermaphrodites or people with significant intersex characteristics? Or people who have all the physical characteristics of a female but have always felt that, deep down, they were a man? Yes, such people are a relatively small minority, but we can’t just ignore them when it comes to gender (or anything else, of course) any more than we can ignore the fact that stars are not where they should be during a solar eclipse according to Newton. Where do these people fit in the binary gender model? They don’t.
Can we find a model of gender that accommodates those who don't fit comfortably in the binary system? In part III, I'll take a first stab at just that.
P.S. For further thoughts on why a simple binary system causes problems, see this recent post at Mormon Matters.