McTeague is a novel by Frank Norris. It follows the story of three primary characters, Mac (McTeague), Trina, and Marcus. Each of the characters wants more than what they currently have. Mac is a dentist who's set in his ways. When Trina comes in complaining of a toothache, he realizes that he needs more in his life. He marries Trina as a way to get it.
Trina is the same way. She marries Mac because she believes that marrying a dentist will allow her to move up in the social hierarchy. However, that doesn't really happen for her. She only feels like she's "made it" when she wins the lottery. Marcus is a friend of Mac's who successfully moves up the social ladder through sheer determination.
None of these characters' stories has a happy ending. They all end in death. Mac kills Trina when she refuses to give up her lottery winnings. Marcus dies after being shot by Mac for trying to take the money. Mac dies handcuffed to Marcus's dead body in Death Valley, where he went to prospect for gold.
McTeague is what's called a naturalistic novel. Naturalism is the philosophical belief that everything arises from natural properties and causes. The school of thought says that people aren't really in control over the circumstances of their lives; nature is. That's why each of the characters' stories ends in death. It's why they all try so hard to get more out of life but fail to do so. They aren't capable of doing so. By showing us that, Norris implies that we should focus on being happy with what we have instead of always wanting more.
Given all that, there are a few different angles you could take with an argumentative essay about this story. You could embrace Harris's naturalistic interpretation of life. You could argue that his depiction of characters and events in the novel is an accurate portrayal of real life. Or you could argue the opposite—that Harris is wrong to state that people have no control over where they end up in life. You could even use examples from the story to illustrate this. For example, Trina and Mac marry. Each of them gets more than they had at the start of the story. They got that by wanting more and by making a decision to change their lives. Does this indicate that people are able to make more changes in their lives than Harris suggests?
The choice is yours. Either way, you'll write a good argumentative essay if you focus on Harris's interpretation of naturalism in this story and on whether you agree or disagree with that interpretation. Best of luck!