Douglass was always considered an intellectual activist and was very respected for the work that he was doing. In this style, he was able to infiltrate the upper epsilons of society and make real inroads towards equality.
The keyword here is equality.
Douglass first appeals to the popular rhetoric at the time that black people were responsible for many problems in society. This captures the attention of those people he wants to influence into level-headed thinkers.
He then adds a list of things that slave owners were doing to black people to draw parallels between the two sets of actions. This not only served as evidence against the hatred and vitriol suffered by so many, but will also appeal to the sympathetic and logical side of his opposition.
His smooth writing style and elegant prose had quite the impact on proceedings at the time because he was able to make educated and balanced comparisons such as this that were irrefutable.