What case for giving women the vote does Jane Addams make? How does she relate her case to ideas about femininity?

Jane Addams—founder of Hull House, a settlement house for poor, newly arrived European immigrants, and co-founded with fellow reformer Ellen Gates Starr in 1889—was a major figure of the Progressive Era. True to her time, she believed that most of the nation's social ills could be ameliorated or eradicated by reforms. She contributed a great deal of her time—never marrying or having children—and money to philanthropy, social science research, and aid to the poor.
She campaigned actively for Theodore Roosevelt and supported women's suffrage with the belief that other women would vote in favor of the social legislation that mattered to her. Some of this legislation concerned neighborhood improvement—that is, the establishment of nurseries, kindergartens, playgrounds, cooperative housing for young women, and the abolition of child labor, to name a few. Clearly, these issues, particularly the care of children, are more often associated with women, or femininity. 
https://www.history.com/topics/womens-history/jane-addams