I think that many American women (and men) are not comfortable with women in the top authority position, with the chief decision-making responsibilities. I do not know what the reasons are behind that--whether there is a belief that women are intellectually inferior (although intellectual brilliance isn't something we seem to prize in our leaders), or (too often cited) women are emotionally incondusive to a position where clarity of thought and cold decision might be necessary, or (and I suspect this might be closest to the truth) Men present an aura (even if illusory) of authority much easier than women do--or are perceived to present that aura.
I read the exchange between you and Irvine and found it interesting and relatively accurate. I think many Americans are comfortable putting women in lesser degrees of authorities (ie, carrying out the policies of the men above them) and can pride themselves by pointing out those numbers.
I've said before I've listened to a lot of talk radio in the past due to curiosity and I'm always amazed by the women who call in, castigating other women for the exact same qualities they orgasm over in men (not that I think a lot of those qualities are exemplary in either sex)
I suppose if you want to take "douse the lights" to a political spectrum (although it is harder to pinpoint in such a broad and therefore hard to watch arena than it is to watch the dynamics in the workplace where you can observe it closely), I would think that you will find it is difficult for women running for higher office to get funding for a campaign without the approval of the male politicians above them. In a recent local election, I listened to the radio campaign a woman running for a state position andinvariably the testimonials from other power figures in the ad came from men--as if she's OK, men approve of her. (The lesser the position, the less the need for male approval).
Interestingly enough, look at two of the women who are in influential positions (one high profile, the other only high profile for a short time), one inadvertently refers to the President as her "husband" and the other practically wrote effusive, almost mash notes to him. I'd be a little hard pressed to find men doing that. My guess is that with politics as in life as I've observed, women rarely get much support or notice unless they are willing to absolutely toe the mark to further the agenda of the male power broker above them and unfortunately adoring deference is part of that recipe. And somehow that is acceptable.