Susan B. Anthony believed that the vote was a right to all women, including Black women. In his speech he makes a connection with the struggle for female suffrage and the struggle of blacks because both women and black people were oppressed and discriminated against by white men, even though they were part of society.
Women and black people had their rights denied through the centuries by a macho and prejudiced society and had to fight against their oppressors to have freedom and the right of their own choices. That is why Susan Susan B. Anthony made the connection in her speech.