I realize that dissecting an image like this one is what earns me the "humorless" in "humorless feminist", but I can't help but notice when the humor in a joke depends entirely on a gendered power differential and our sexist history.
You see, this wouldn't be considered funny if women's suffrage had never been in question, and the fact that the 19th amendment isn't even 100 years old yet makes gags like these especially damaging to women. Not only does the phrase "men's suffrage" carry no similar meaning, but because men are considered the default and women are "other", individual men aren't considered as stand-ins for all men. They get a free pass on that burden.
It's the exact same principle at work.