To convince and persuade
Usually a conventional, thesis-driven essay — the conventional academic model has an identifiable thesis, intro, body, conclusion, like the example in your St. Martin’s Handbook; our Op-Ed model is more flexible
More often than not, out-and-out defeat of another — as in a debate, for example — is not only unrealistic but also undesirable. Rather, the goal is to persuade readers to see an issue in a particular way, or to help them understand, or move them toward some action, or to cause them to be newly interested in your issue.
To reach a decision or explore an issue
This is where we get to see the writer struggling with an issue and engaging in truth-seeking behavior
Often, a writer must enter into conversation with others and collaborate in seeking the best possible understanding of a problem, exploring all possible approaches and choosing the best alternatives. As all good critical thinkers know, there’s always more than just one side of the story, there’s always more than two sides of the story: there’s always a third side of the story. Some people phrase that as “there’s your truth, there’s my truth, and then there’s the real truth.”
To change yourself
We can think of this one as the “Leslie Jameson model”
Sometimes you will find yourself arguing primarily with yourself, and those arguments often take the form of intense meditations on a theme, or even of prayer. In such cases, you may be hoping to transform something in yourself or to reach peace of mind on a troubling subject.
From your St. Martin’s Handbook — 2.9a “Arguing for a purpose” (p. 186)