The correct answer to this open question is the following.
The two arguments in favor of lighting for female suffrage in the mid-1800s would be these.
1.- Women are equal to men, so they deserve the same rights and obligations under the law.
2.- Women played an important role not only in the family but also were smart enough to be included in the business and social life.
The two arguments against female suffrage would be these.
1.- Many anti-suffragist of that time said that most women did not have the desire to vote.
2.- Unfortunately, some of those anti-suffragist believed that women did not have the expertise or intellect to be informed about politics. Some of the formed associations such as the Massachusetts Association Opposed to the Further Extension of Suffrage to Woman.
Fortunately, as we know, the 19th Amendment to the United States Constitution granted American women the right to vote in August 18, 1920.