Final answer:
Susan B. Anthony reasoned that the 14th Amendment implied women, as citizens, had the right to vote. Elizabeth Cady Stanton and other suffragists highlighted the inconsistencies and prejudices in the arguments made by opponents of women's suffrage. Despite legal setbacks, their activism contributed to the long-term fight for suffrage for women.
Step-by-step explanation:
Susan B. Anthony used the logic that women, as citizens, already possessed the right to vote based on the 14th Amendment, which guaranteed equal protection under the law. She, along with other suffragists, argued that if women were citizens, they should automatically have the right to vote, a concept partly inspired by the republic's formation in protest of taxation without representation. Despite the Supreme Court ruling in Minor v. Happersett that suffrage was not a guaranteed right of citizenship, Anthony and others continued to challenge assumptions about gender and democracy through legal action and activism.
Proponents like Elizabeth Cady Stanton and Sojourner Truth used their intellect and knowledge of history to expose the flaws in arguments against women's suffrage and the hypocrisy of men who claimed to oppose it for the good of womankind. Stanton notably argued against the paternalistic views that restricted women to a 'female sphere' and advocated for the right of women to judge their own roles, which included voting.
Hannah Corbin and others highlighted the inequity in preventing single, property-holding women from voting, while still taxing them, and suggested women should have the right to vote or be exempt from taxes on their property. This reasoning, and the activism of women following it, laid the groundwork for challenging and eventually changing the legal and social barriers to women's enfranchisement.