Rebuttal

Rebuttal is the process of proving that the opposing team's arguments should be accorded less weight than is claimed for them. It may consist of:
•    showing that the opposing argument is based on an error of fact or an erroneous interpretation of fact;
•    showing that the opposing argument is irrelevant to the proof of the topic;
•    showing that the opposing argument is illogical, i.e. it involves some form of logical fallacy;
•    showing that the opposing argument, while itself correct, involves unacceptable implications;
•    showing that the opposing argument, while itself correct, should be accorded little weight;

As with arguments, assertions do not equal rebuttals. Just as teams must show how and why their own arguments are valid, so they must show how and why the opposition's arguments are invalid:
•    an argument may be wrong in fact or logic — if so, say how and why it is wrong;
•    an argument may contradict their theme line, or something else a speaker on that team has said — if so, point out where the contradiction lies;
•    an argument may be true but completely irrelevant — if so, point out how the argument is irrelevant (irrelevant arguments are often called red herrings).
It is not necessary to rebutt every single point and fact raised by the other side. Single out their main arguments and attack those first. Savage their theme line and show how it falls down — and show why yours is better! Apart from argument-by-argument rebuttal, you should also try to provide a general rebuttal for the whole case of the other team.