While it is possible to write an argument without answering the points that will be made by a writer with opposite views, it is much better to refute those points in the course of your composition. Ignoring a major argument of the other side leaves you in a weak position. Your success in persuasion may depend on how well you can answer opposing arguments. Therefore, in planning an argumentative article, consider carefully what can be said against your views, and prepare a strong reply.
Chapter 23 Language and Logic in Warriner's English Grammar and Composition Revised Edition, Complete Course, John E. Warriner and Francis Griffith, 1965