In drafting a respondent's argument, the task, at first glance, is fairly simple: emphasize the stringent standard of review, refute each of appellant's contentions point by point, distinguish the cases relied upon, cite a few of your own, and conclude by requesting that the Court should affirm the judgment below.
This represents the basic outline in drafting a respondent's brief, and will remain so as long as law schools are teaching the IRAC approach to constructing legal arguments. Blindly adhering to this format, however, will cause you to overlook some dispositive issues that could enhance the quality of your brief.
Say that the appellant claims that the trial court improperly admitted gruesome photographs into evidence. One would hope that the appellant's attorney would confront the harmless error issue head on, but we all know that the best practices of the profession are not borne out by reality. When faced with a choice of confronting a counterargument - here, overwhelming evidence establishing defendant's guilt or liability - or simply ignoring the issue, the typical attorney will all too often opt for the latter, hoping that opposing counsel will fail to spot it. If you are bent on merely responding the narrow question - constructed by appellant no less - of whether the photographs were unduly prejudicial, you have conceded the field of battle to your adversary's turf.
This highlights the importance of establishing your affirmative case. As respondent's counsel, free yourself from the intricacies of appellant's argument and ask the simple question of why fairness and justice dictates a result in your favor. Reformulating the question in this manner will compel you to examine all the evidence from a fresh and holistic perspective. In turn, you will uncover new avenues for research that will greatly improve your theory of the case.