That comes from a poem I once wrote, because in ballroom dancing men lead and so they do in arrogance. Arrogance is a necessary ingredient for success and women, on the whole, have too little of it (except, possibly, in the field of child-rearing). I'm not going into the reasons for that here, partly because you can list them as well as I can. What I wish to address is the definition of arrogance in this post and why it matters.
For the duration of this post, then, arrogance means an untested and possibly baseless belief in one's own abilities. Arrogant individuals believe that they are great and that they can take on any task they are offered. Whether this is at all true depends.
Women tend not to have this kind of arrogance as often as men do, and this is one of the reasons why women submit fewer manuscripts to newspapers, send me fewer e-mails about their great blogs or in general push for the position, job or salary increase they might deserve. I think this may also be the reason why women sometimes appear to blossom later in life. Once you see what various arrogant individuals actually achieve you may start feeling freer about flaunting your own stuff.
That's how far I had thought out this topic before attacking the keyboard, but now it occurs to me that the definition of arrogance I'm groping for should include something about the competition. It's not just that some individuals have greater self-confidence in their own abilities; they also discount the abilities of others (or perhaps not to consider them at all). In some sense I've been the reverse of that, always expecting someone else to turn up with the arguments I wanted to read.
Now is this more common among women than men? It could be, which might also explain those lower rates of women agreeing to be the expert on some panel discussion, say. And if so, how can the "arrogance gap" be narrowed? Are women more afraid of the crash which will happen if the arrogance turns out unwarranted? Is that crash larger for women, on average?
I don't think the difference in arrogance is just a corollary of different risk-taking characteristics of the sexes, say, because my definition of arrogance is about an underlying difference in the reading of one's own abilities. Arrogant individuals are not just more eager to leap on the horse; they also believe that they are better riders. Whether they are or not doesn't really matter here.
Then finally to the reasons why I'm talking about arrogance rather than about a healthy self-esteem. The latter is insufficient if one esteems the skills of others too highly, and it's also insufficient if others esteem their own skills too highly. What we need is a spoonful of real arrogance.