So what the heck is this "concession" stuff all about?
It is often important to make a concession to the other side to make your argument stronger—that is, rather than acting like another side of your argument does not exist, you address it and “debunk” it. In fact, in an argument paper, presenting the other side and then “tearing it apart” can often be a very effective strategy. Conceding to some of your opposition’s concerns can demonstrate respect for their opinion. Making concessions also demonstrates your ability as a writer by showing that you have researched and considered you argument from multiple perspectives in order to come to an informed decision.
Naturally, what you don’t want to do is present a counterargument and not address it. It might be tempting to do this in your conclusion; you may feel that you’ve made your point pretty strongly and that it is okay to just say something about the “other side” and just leave it there. But resist—the conclusion is what the reader is left with.
There is no surefire way to make concession, but it is likely a good idea to keep it short, limiting yourself to one per paragraph at the most (otherwise the counterarguments and concessions start to become your argument). Also, watch out for fallacies—sometimes it might be tempting to make a bad analogy or to oversimplify in order to “dismiss” the other side. Basically, if you can’t make the concession strongly, it may be better not to address it all (emphasis added).