Does sociobiology have anything to say about this? What about the impact of being a mother; does that have an effect?
Well, as a general rule, I’d say yes. Most libertarian thinkers and politicians are men, and the same thing goes for conservatives. Women, when they are politically active, almost universally seem to join the left. Hillary Clinton, Emma Goldman, Helen Clark, Golda Meir, Jiang Qing, Ariana Huffington.. the only conservative women who I can think of off the top of my head are Ann Coulter, Michelle Malkin, Laura Schlessinger and Sarah Palin, and I can’t think of any libertarian women.
Of course, correlation does not prove causation, so having an XX chromosome doesn’t necessarily make one inclined to leftism. But at least as of the present, the historical trend is for politically active women to be left wing.
Short of peer-reviewed empirical research, you have only your own anecdotal perceptions to guide you to an answer. My own yield the result that there are more male than female self-identified libertarians of any stripe, and that goes with radicalism in general. I don’t know why that is, but sexist insinuations that women’s softness and emotion lead them to the left en masse will probably ensure that that stays the case.
Fewer than 20% of new engineering graduates are women. Men make up 90% of doctoral engineers.
I tried to google what the gender gap is in liberal arts majors, but it just brought up a bunch of African American Women’s Studies programs.
Wendy McElroy, Isabel Paterson, and Rose Wilder Lane all spring to mind immediately.
But what about in general? I mean if you were to ask 10 men at random and 10 women at random would there be a substantial difference in the number of self-identified libertarians between the genders?
Obama approval is always 6 points higher among females
http://www.gallup.com/poll/121199/Obama-Weekly-Job-Approval-Demographic-Groups.aspx
Also, Mary J. Ruwart. Yes, they are rare but they do exist.
I believe that women tend to care somewhat less about politics in general, and when you care little about something yet it is considered imperative to have some view on the subject, you just grab what is receiving the most publicity: hence women tend to the left, but few will entertain a lengthy debate on the subject, I suspect.
From a young age, females are pushed to be pretty instead of to think (even less than males).
Libertarian women can be amazing:
LOL, I blazed it with her and Scott Horton. So don’t get me wrong; I don’t let ideology get in the way of personal relationships. 
. Not very nice to give names. what is your real name blazer?
Julian Enrique Gutierrez Aldana, son of Norma Lisette Aldana Rodriguez and Salvador Grajeda Gutierrez. Why do you ask?
The state has a long reach. If you violate its laws it can and will put you in prison. Why give someone’s real name, beside your own. I would be pissed. Give your name as much as you want. Give others the same courtesy, that is all.
It depends on what is significant. At random, if you ask 10 men or 10 women if they are libertarian, your results would probably be 0 for both.
Yes, and my own written claims on a forum that someone smoked marijuana are certainly enough to get them 20 to life, aren’t they? 
Women are more left than right for a number of reasons. Women are the motherly figures, “caring”, “loving” and looking out for everyone, much like the democratic party who helps the poor, disadvantaged, etc, from a number of troubles whereas conservatives/libertarians appear cold blooded and resist much more visible forms of help. Most women support “progressive” policies (child labor laws, worker regulation, anti discrimination laws) that go directly againist libertarian policies and their support for “dog eat dog” capitalism. In addition, mainly because of the mother-son link, most women are anti-war, and as such go to the left instead of the right because liberals “appear” to be more anti-war than conservatives. You also have the big ticket items, like abortion, which from at least my experience most women believe is their decision, and the overall image of liberalism, which promotes change and breaking the status quo of female discrimination, etc etc, something that conservatives and libertarians don’t seem to care too much about.
I’d be interested to see this discussion resurrected. (The OP one, not the tangent.)
I think there are attempts from social scientists to research this.
for example
Abstract
Studies carried out in many countries in previous decades found that women were more conservative than men and less likely to participate in politics. Here, it is examined whether this traditional gender gap persists today, or whether gender cleavages in the electorate have converged, and whether the phenomenon of the modern gender gap, with women more left wing, has become evident elsewhere. The article draws on evidence from the World Values Surveys in the early 1980s, and the early and mid-1990s carried out in over sixty countries around the world. This study establishes that gender differences in electoral behavior have been realigning, with women moving toward the left of men throughout advanced industrial societies (though not in postcommunist societies or developing countries) and explores the reasons for this development, including the role of structural and cultural factors. The conclusion considers the political implications of the findings
I don’t think sniffing up sociobiology is going to lead to many good answers. It seems like a form of scientism.