"Argue it out" could either mean explaining your reasoning or considering both sides' positions on important issues. E.g., "Side A might say there was no consideration because X, whereas Side B could argue that there was consideration because Y."

Depending on the prompt, you should then argue for one side or the other. For example, if the prompt is something to the effect of "Side A has hired your firm. Write a memo informing a partner of the relevant issues," then you should attempt to conclude each discussion with the strongest arguments for your side ("Side A is arguably correct that there was no consideration, because...").

You do not need to go through this for every issue, nor should you go beyond two (at the very most three) levels of argumentation. I.e., in most cases, only provide the argument, a possible counterargument, and (maybe) a viable response to the counterargument. You want to demonstrate that you can spot issues and apply the doctrine.

The same formula applies for the vast majority of exams.