The connection between classical liberalism and women's rights is so strong that the really baffling thing is how long it took people to see it.
Classical liberalism was based on principles like personal freedom, equality of opportunity, and universal suffrage---and yet for centuries these principles were only applied to upper-class White men.
Even as the Declaration of Independence said "all men are created equal", policy did not even actually include all men for a long time---much less all human beings as it should have said in the first place.
There was of course no logical reason to justify this; it didn't make sense in terms of the principles of liberty to systematically exclude so many people. Some of the first modern arguments for women's rights were based on classical liberalism, and in terms of logic they were basically irrefutable. On any rational account of individual rights, all human beings would be included. On any rational account of democracy, all adults would have suffrage.
The problem, of course, is that human beings are not pure rational agents, much as we might pretend ourselves to be. We often behave irrationally. In this case, the irrational refusal to accept women and people of color as full human beings and equal citizens caused an enormous amount of suffering around the world for centuries---and in some cases still does today.
The inclusion of women and people of color as citizens and voters was a major step forward toward the goals established by classical liberal principles centuries ago. It's just a shame that it took so long to actually apply those principles consistently.