Elizabeth Cady Stanton was a racist and a man-hater. She authored this as part of her jealousy of the movement to give Black people the vote.
Not once had she ever fought to be part of the militia (which was a requirement for voting) yet she wanted the same rights and privileges of the men who fought and died for the United States.
She saw herself as the leader of a supremacy movement in which men would die in labor and combat to serve her interests and the interests of her followers. "Women are infinitely superior to men." was one of her battle cries for setting up a system in which women had rights and immunities superior to men, while men had all of the responsibilities in our culture.