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.