Chapter seven is about the different ways of constructing arguments."The key to Rogerian argumentation is a willingness to think about opposing positions and to describe them fairly"(177). The Rogerian argument is about having a full understanding of the subject you wish to talk about and looking and explaining it from different point of views to make an argument. It's important to go in depth with the subject to get a deep understanding. How would you know what's best if you don't know everything about it? This provides ethos for the readers it lets them know you know exactly what you're talking about. It may be kind of challenging to write about the pros and cons from each point of view, yet, explaining how your point is better than all of the ones you've listed. It's better to compromise and build a common ground with the reader to strive for solutions that can benefit everyone. In my opinion, I think this would be more difficult, especially if you're very opinionated.
Another argument mentioned is the Toulmin argument, which is about having a clear understanding of a subject but worrying less about the readers reaction, whether they agree or disagree it's about justifying your ideas.
Toulmin Argument Outline:
-claim (what's being argued)
-qualifier (limit the strength of the argument)
-good reasons
-warrant (logical statement connecting the claim and data)
-backing (prove the warrant is true by the use of evidence which also leads to authority)
-rebuttals (counter-arguments, as if the argument isn't true)

For our next project I plan on writing about Marijuana,
here is my quick Toulmin argument outline:
claim: Legalization of Marijuana in the United States (Pro Legalization)
reason: Marijuana is harmless
warrant: since it relieves the pain of cancer patients and is less risky/addictive than the use of alcohol, tobacco, and other nonprescription drugs.
backing: It has been made legal in certain states for medical purposes and proves to help relieve pain and stimulate appetite. If the United States can legalize other drugs and the use of alcohol surely they should legalize marijuana, it's one of the safest drugs out there. It can benefit us medically and economically, it can also improve society.
rebuttals: Marijuana is a hallucinogen and has THC in it. It is an illegal substance that no one should use.
qualifier: Marijuana is harmless SO it should be legalized.
authority: U.S. Government