Think it was called Marriage.
By what metaphor did the queen become equated with mobility and power?

The King is the leader of the army, and without leadership the army would be useless. But as one man, the leader is relatively powerless. As for the Queen... I mean this in a factual nice way, but women are incredibly manipulative. It's in their nature, and it isn't a negative thing. (Unless it is used for the 'wrong' purposes...) Manipulation is changing things, which is exercising power. So in a way, women are all powerful, and maybe that's why the Queen is the most powerful piece on the board.
My dad had 7 sisters, and was as feminist as a man could reasonably be. Meaning that I grew up believing women my equals in every sense. I also read in the Handbook to Higher Consciousness by Ken Keyes, Jr. once that most of the personality differences that people ascribe to the sex differences between men and women actually go both ways. And considering that, I realized that if one really takes a good objective look at it, one can can see countless exceptions to the men vs. women stereotypes that prevail in society. I see women excelling at things that are typically male dominated and vice versa. I see men gossiping, and women who are short spoken. I see women CEOs and men making excellent nurturers of children. I see women with spotless driving records and men with tickets and DUIs. I see women who are scientists, engineers and intellectuals and I see men who are emotional sensitive artists. I don't see any benefit for the most part in distinguishing men or women from our humanity in common for most things. There are a few situations I consider the distinction helpful however ;-)
Besides sexuality itself, one thing I find in my own marriage and from other relationships is that the women I've been with are generally a bit more grounded and focused on common sense than I am, and better multi-taskers, but I've no doubt whatsoever, that there are plenty of men who fit the bill as well and women who don't.
I just wonder what was going on in contemporary society in the era modern chess developed, that made it commonly accepted that the Queen would be a piece that had so much power and mobility, compared to the relatively weak but all-important King.