I’m a guy, and I don’t particularly like to shake my groove thing in the club style dancing. However, I’m not opposed to learning dances like waltzes and tangoes and the like. I took swing dancing lessons in college for a while, and there were definitely more girls than guys there. At the time, I didn’t question it because hey, more girls.
I will admit, though, that seeing women solo dance in rhythm with songs is extremely awesome. 
Women who can’t dance will still dance.
I’ll go out on a limb and say the tendencies are gender related. By that I mean the desire to dance is more gender related. Women are driven to be desired and men to desire. It’s not a mutually exclusive set of behaviors but the tendencies are there.
Dancing is a mating ritual that serves as a visual queue to join in and, once engaged, a method to observe and touch the potential mate.
On a side note: I was watching a bunch of women dancing together a couple of weeks ago and observed a distinct pattern of behavior. When one dance partner strayed toward another person (man or woman) the woman she started dancing with would furrow her brow in annoyance and then reach for her elbow in an attempt to reel her back in. I observed this in 3 different women and it was immediate and obvious. Since 3 people do not make much of a sample I will look for this at different venues to see if it occurs elsewhere.
Women when dancing tend to be very protective of one another. It’s possible that furrowed-brow dancer thought straying dancer was getting too close to the danger zone - that part of the dance floor where someone will assume you’re alone and start grinding on your ass uninvited.
Lots of the time when we’d go clubbing, my friends would also work as a sort of checkpoint. Their brows would furrow, all right, as they very subtly chased off men (and women) they deemed unworthy of me! 
I’m a gal and I like to dance, but I’m pretty self conscious about it in public so I only dance if I have a load on, unless I’m in a situation where I have to. Then I still suck because I am really uncoordinated.
Most guys I know, loaded or not, don’t like to dance. The guys I grew up with had to dance on many occasions (stuff like waltzes and cha-cha) but I can tell you that the guys I knew didn’t like it. In fact, I have only met one guy in my life who liked to dance. I used to date him and he was an excellent, coordinated dancer.
Bleah, the bastard put me to shame. 