The thing that struck me about the Turing Test, when I heard about it, was the crazy thought: how do I know that other people are anything like me? If we can't even judge faithfully between ourselves, how can we judge between humans and computers? For I can do nothing but observe reactions, the effect of my actions on others. I can't read people's minds: they could, for all I know, run entirely different mental software. Everyone is, in some sense, a black box.
The act of empathy, then, is a little presumptuous and magical: I trust that we can share an understanding with each other, with the assumption that because I share a similar hardware architecture with you, that there's a very strong chance that I share the same kinds of thoughts and values too. I think that's why we put so much emphasis on physical bodies. If someone looks different, I may fear them: they don't look like me, and so they might be thinking in an entirely different way. We all know the dilemma of the Turing Test deep in our bones, and we cheat a little (or a lot) by using irrelevant physical similarities in our judgements of one another.
I suppose I could be silly and wry and conclude that this is why women are mysterious and terrifying to me.
But I think that there's something there that deserves more serious thinking.