Bryan Caplan thinks he can explain why there is a gender gap among libertarians (along with a few other gender gaps):
My study of personality psychology makes me one of the doubters. On the popular Myers-Briggs personality test, there is a huge Thinking-Feeling gap between men and women. For men, the breakdown is roughly 60% Thinking, 40% Feeling. For women, the breakdown is roughly 30% Thinking, 70% Feeling.
This Thinking/Feeling disparity explains a lot about gender gaps in college major and occupation. There’s every reason to think that this disparity can help explain gender gaps in political and social views.
To make a long story short: Thinking people tend to have “hard heads” and “hard hearts,” while Feeling people have “soft heads” and “soft hearts.” Unsurprisingly, then, Feeling people tend to hold more anti-market views. I’ve similarly found strong evidence that males “think more like economists.” This gender belief gap increases with education, consistent with a simple model where male and female students gradually learn more about whatever their personalities incline them to study.
The whole premise “Bleeding Heart Libertarianism,” of course, is that we should unbundle the hardness of our heads and the hardness of our hearts. Logically speaking, we can combine hard heads and soft hearts. Empirically, though, this combination is rare. And that’s why Bleeding Heart Libertarians have their work cut out for them. If you’re trying to sell libertarianism to Feeling people, “hard head, soft heart” ideas are more persuasive than “hard head, hard heart” ideas. But the libertarian remains at an inherent disadvantage against intellectual rivals pedaling “soft head, soft heart” ideas.