The need for forceful language arises from several conditions.  The first is that the narrative, first and foremost, is a personalized expression of voice.  Douglass is not writing a dissertation or some type of detached analysis.  He experienced what it means to be a slave.  Accordingly, there is natural emotion present for it is his voice and expression of subjective reality being articulated.  When a victim of violence is expressing what they endured, there is emotion to be expected.  At the same time, Douglass is mindful of the hypocrisy present in a nation that condones and allows slavery to exist.  The emotional and intellectual response converge in the need to utilize forceful language to explore the dynamics between fully understanding how a nation predicated upon "liberty and justice for all" and "all men are created equal" ring quite hollow in a nation where slavery exists.  Douglass' use of forceful language helps to identify how the presence of slavery undermines the very goals of American political thought and American social ideals.

If Douglass did not use forceful language then the passion in his speeches would not have shown through. He endured many hardships during his life. He encountered people who believed that black people were beneath dogs and he met people who believed that black people deserved every right that white people did. Many people even believed that there was nothing wrong with slavery but slaves should just be treated more fairly and not abused.

Douglass was a very intelligent man and an excellent speaker. Of course he had passion for his cause. If he did not, his speeches would have been boring and he would not have had the impact that he did.

I believe that you are asking about something that Douglass says in his Fourth of July speech at Rochester, New York.  In that speech, he says "I will use the severest language I can command," and I think that is what you are talking about.

He believes that he needs to use this kind of language because of how evil slavery is.  He does not think you can sugarcoat it at all.  He thinks that he must speak out and say that slavery is opposed to what America is about and that it is opposed to what Christianity is about.

Because he thinks it is so evil, he feels he must denounce it as strongly as possible.

I don't know that he feels he needs to or just feels that forceful about the subject of slavery.  Remember all that he's survived, and then even after he escapes to the North he encounters people all the time who do not think slavery is that bad, or that morally wrong.  I can't imagine how angry that would make me if I were him.  There is also a sense of urgency about Douglass, as he knows that America "drinks daily the warm blood of my outraged brothers and sisters".  He feels that there is no other way to express such an abominable crime as slavery except in the strongest possible terms.

Why does Douglass believe he needs to use forceful language?from The Narrative of the Life of Frederick Douglass book

I'm amazed Douglass didn't use forceful language in everyday conversation, given the horrors of his upbringing as a slave, and a runaway slave recaptured, or a slave sent to the "slavebreaker". 

Douglass had to feel outraged and incensed that, even in the North, in the middle of a supposedly Christian nation, people weren't more outraged and willing to do what was necessary and right to end the institution.  Some people even called him a liar, saying he was so well spoken and well written that he could never have been a slave.

On a more practical level, I think he felt, like Garrison and John Brown, that Americans needed to awaken, and that he could shout and shock them awake with his speeches and his writing.