Calvin Olsen, College Professor, Poet, and Editor
There is some great advice on here (which is proof that you’ve asked an excellent question), and although I’m a little late to the game, here’s a more specific formula for building a counterargument into your essay. When I teach a writing course, I require counterarguments in every paper over four pages. The best approach to a counterargument is called “Acknowledgement and Response.”
Some people worry that a counterargument undermines their argument, but as you’ve learned in the other responses here such is not the case. The trick is to prove that you know your stuff—you’ve done your homework and you are aware of how your particular argument fits in the grand scheme of things. As you do this, you gain the trust of your reader/audience, which is why Acknowledgement is so important. Give your naysayers credit: they’re not stupid, and they’re not uninformed, so their side of the argument is as valid as yours. To acknowledge them, you simply let them know that you understand where they’re coming from. Even an phrase like “Some readers believe [insert their argument here], which makes sense when we consider [insert their evidence here]” will let them know that you hear them. You acknowledge the argument and/or point, and the knowledge that you’re also informed will help them at least listen to your response.
The Response portion of the counterargument is a little easier, because you are more flexible in what you can say (which is what we all want to get to anyway). Once you’ve finished Acknowledgement, you can throw in a “but” or a “however” and the floor is yours. It’s important to remember that your response gains power the more specifically you connect it to the argument you acknowledged. If your response to Americans that prefer Pepsi over Coca-Cola is that they should be drinking more water, they’re not going to give you any credit. But if you get specific—say, telling Pepsi drinkers that travel frequently that Coca-Cola is actually easier to find in other countries—they’ll know that you both understand the argument and their point.
To sum up: take a look at what your argument is, choose a counterargument that relates specifically to yours, give your reader credit for being informed, and then provide specific evidence that help sway them to your side.