That really about sums it up. Men tend to be more aggressive and therefore value freedom relatively highly. Women tend to seek security and value it more highly than freedom.
You can explain it on grounds of evolution, cultural mores, childbearing and rearing, physical strength, hormones, sex-roles, whatever. They all lead to the same outcome.
There are of course many exceptions to the rule, but those women who do not have security provided by a man or a family tend to seek it where they can, often from government. Men tend to be more self-reliant (or else self-destructive).
Voting patterns just follow.
In my way of thinking, murder is murder, whether it is three months prior to birth or one month after ... but then, that is just my view.
As a single woman and a former lib who's now seen the light, I think you are right. I think women in general feel more vulnerable than men. While men tend to think, "Oh, no, another big government program, more big government breathing down our necks," women tend to think, "Gee, I might need that program someday."
Also, a lot of women are taken in by the big lie that Republicans are just a bunch of selfish, mean-spirited old white guys who want to keep women barefoot and pregnant-- while the libs are the open-minded, compassionate ones who will help women and children. It's not true, but that's how a lot of women think. I think the tide may be turning, though-- more women are wising up and seeing the light.