There are generally two methods by which you can challenge an argument. First is by challenging its logical structure, either by its premises, conclusions, or use of various logical fallacies. This is effective when you are debating people like Howard Dean, or your local college student, who sputter nothing but arguments dripping with fallacious reasoning. However, when you are debating more well-reasoned individuals, as you should be doing, you may need to apply the second technique, which is to concede a point yet offer a stronger alternative.