Here's a particulary clear explanation of how to deal with Counter Argument:
Rebuttals and Main/Faulty/Return Paths
Unlike many forms of writing, academic arguments will often include discussions of possible objections and counterarguments to the position being advanced. Academic arguments typically take place in disciplinary communities in which a variety of competing or divergent positions exist. When preparing to 'speak' to the community by writing an argument, writers are aware of the arguments against which they must build their claims, and of the counterarguments which are likely to emerge. Dealing with counterarguments and objections is thus a key part of the process of building arguments, refining them, interpreting and analyzing them. There are several main reasons for introducing counterarguments and objections.
1. It demonstrates that the author is aware of opposing views, and is not trying to 'sweep them under the table'. It thus is more likely to make the writer's argument seem 'balanced' or 'fair' to readers, and as a consequence be persuasive.
2. It shows that the writer is thinking carefully about the responses of readers, anticipating the objections that many readers may have. Introducing the reader to some of the positions opposed to your own, and showing how you can deal with possible objections can thus work to 'inoculate' the reader against counterarguments.
3. By contrasting one's position with the arguments or alternative hypotheses one is against, one clarifies the position that is being argued for.
When dealing with objections or counterarguments, authors tend to take one of 3 approaches.
Strategic concession: acknowledgment of some of the merits of a different view. In some cases, this may mean accepting or incorporating some components of an authors' argument, while rejecting other parts of it.
Refutation: this involves being able to show important weaknesses and shortcomings in an opponent's position that demonstrate that his/her argument ought to be rejected.
Demonstration of irrelevance: showing that the issue in question is to be understood such that opposing views, while perhaps valid in certain respects, do not in fact meet the criteria of relevance that you believe define the issue.