A good argumentative paper always includes the other side's arguments, even--especially, actually--if you don't think they are valid.
Yes, that's an important point. I learned it as "refuting the counter-argument." I don't think Susan intended to suggest that it is wrong to attend to the counter-argument; that is part of backing up the thesis argument. I'm glad you mentioned that here, an important point. I might refer people to this thread for these explanations of the counter-argument.