There are two primary themes in Edward Arlington Robinson's poem "Richard Corey," and both of them would make good topics for a persuasive or argumentative essay. The poem is not very long and does not contain much action; however, what does happen is significant.
Richard Corey is described with very noble and kingly imagery. He is a "gentleman from sole to crown," "imperially slim," and "richer than a king." He glitters when he walks, is schooled in every grace, and people are moved by his presence. Even his name is a kingly one.
In fine [in short], we thought that he was everything
To make us wish that we were in his place.
The people envied Richard Corey because he was everything they were not. Their lives, in contrast, are dull, ordinary, and difficult:
So on we worked, and waited for the light,
And went without the meat, and cursed the bread.
Obviously, though, Richard Corey did not see himself as others saw him, for
Richard Cory, one calm summer night,
Went home and put a bullet through his head.
The first theme you could explore in an argumentative or persuasive essay is that we should not judge a person solely by appearances. By all outward measures, Richard Corey has everything anyone can want and people envied him; despite that, Richard Corey was not happy. In fact, he was so miserable and discontent with his life that he committed suicide.
A second possible theme is that wealth and position and even personal magnetism cannot ensure happiness. Clearly Richard Corey had everything that others wanted to have and be, but none of it made him happy, In fact, he was so unhappy with his life that he wanted to end it.
So, you could use this poem to make the case that it is not wise (or accurate) to judge people based only on what is on the outside: appearance, money, talents, and other external factors. I'm confident you can think of plenty of reasons and examples to prove this point.
You could also make the argument that possessing things (wealth, beauty, popularity) does not constitute happiness. Again, you can undoubtedly think of many examples to prove this point.
Both of these basic ideas would be terrific starting points for a persuasive or argumentative essay. To help you, I have attached an excellent eNotes site (linked below) on how to write an argumentative essay in nine easy steps.