You're missing what the 19th amendment fundamentally is:

The Nineteenth Amendment (Amendment XIX) to the United States Constitution prohibits the United States and its states from denying the right to vote to citizens of the United States on the basis of sex, in effect recognizing the right of women to vote. The amendment was the culmination of a decades-long movement for women's suffrage in the United States, at both the state and national levels, and was part of the worldwide movement towards women's suffrage and part of the wider women's rights movement.