Anthony declares that if women are prevented from voting, then the United States is not truly a republic but, rather, she says, "It is an odious aristocracy; a hateful oligarchy of sex; the most hateful aristocracy ever established on the face of the globe; an oligarchy of wealth, where the rich govern the poor." An aristocracy is a kind of political system wherein an upper class comprised of those who have hereditary titles or offices are entitled to rule; Anthony's metaphor draws attention to the fact that men have done nothing to deserve their right to vote any more than aristocrats have done to deserve their right to rule. Men rule simply because they are men, and this is not just.
A metaphor is a comparison of two unalike things where one is said to be the other. In an oligarchy, a small group maintains control of the country. Anthony's metaphor compares the American democratic system to an oligarchy because only men are allowed to vote, maintaining control of the country that women helped to build. Further, the rich are permitted to govern the poor. She seems to suggest that the United States cannot properly call itself a democracy when it withholds the right to vote from half of its population merely on the basis of sex. She compares it to an oligarchy because simply being a (white) man seems to guarantee one the right to govern.