First, this is a long comment, and I don't want to come off as dissing it. I agree with you. Except for that concluding thought.

I used to think that that was true, women vs. men for voting rights. But about ten years ago, I wandered into the Berkeley Historical Society. They had a bunch of materials on display about the women's suffrage movement, including just boxes of documents. One of the first ones that I pulled out was a poster for an anti-suffrage meeting. A meeting organized by women.

In fact, they had lots of documentation about anti-suffrage efforts by the society women of Berkeley. That completely shocked me, given Berkeley's crunchy reputation. But I did more research later, and found that it was not at all unusual.

Up until the early years of the 20th century, most women were against it! Even when the 15th Amendment passed, a large minority of women still opposed it. As well, quite a lot of men supported it. (Obviously, they had, to since they were the ones voting to pass it.)

Anyway, the framing of the issue as women demanding the vote from men is oversimplified.