To examine and rebut the opposition's arguments, you need to question the evidence and the general conclusions drawn from that evidence. Address whether the opposition oversimplified or understated the alternatives. Question how the opposition used the logical and ethical arguments and plays on the readers' emotion to build their argument. Question the conclusions drawn by the opposition and how they persuade their audience to a specific course of action.
Since you will need to present all ideas in a fair and rational way, you need to anticipate the arguments on both sides of the issues. When you argue for the superiority of one position over another, you need to present its strengths and weaknesses. This usually entails addressing the opposition's perspective on the topic in detail, using your superior position as the reference point. If you are presenting the facts and not taking one position or another, you need to present the strengths and weaknesses on both sides of the argument, critically evaluating the ideas, evidence, claims, methods, and conclusions.
Making a list of strengths and weaknesses for each position is a good start to understanding the problem at hand. As you make your list, be sure to take notes about where you found the information and whether what you have written is a quote, paraphrase, or summary.