One, you can admit their points. Concession won't invalidate your argument necessarily, but it may well make it less unilateral. Your third option in considering the opposition is refutation. Show the arguments of the opposition, and overcome them by showing their limitations. In many cases, considering the counter arguments blends these three options.
Counter arguments can strengthen our own arguments.
Even if you judge some parts of the opposing argument illogical, you may find merit in some of their claims, merits that can improve the case you're making. That still makes sense to me. Here's another example of the use of counter argument in advancing an argument. This one is an argument against lowering the drinking age . The ten-page requirement applies to the text itself, not the Works Cited pages nor any appendices you may wish to include.