Susan B. Anthony believed she had the right to vote because she heavily believed men and women were equal and there was no reason why women should not have the right to vote. She is a very prominent figure in women's suffrage. She dedicated her life to trying to get equal rights for women and even founded the National Woman's Suffrage Association.
When she ended up voting illegally, she was fined. She didn't pay this fine and she even ended up going to jail and was found guilty of voting illegally. This did not stop her though, no matter what she wanted equal rights for women.
Even after Susan died, many women continued in her shoes to try to finish what she started. Years later, the Nineteenth Amendment in the United States Constitution was ratified, this made it so anyone could vote regardless of gender.