A counter argument is necessary, in order to show one's audience that one has taken into account the opposing opinion/thesis of the argument but still sides with their opinion/thesis; it allows the writer to once again prove their thesis.
Well, it depends on what kind of situation you're in. But the best advice is to handle it the best you can. If you really have no idea how to improvise in the situation, search on the internet to see if other people have experienced what you're going through, and follow some advice that would seem like it would really help in your situation.
