Right, how highschool debate should be structured is like this:

Two parties are given sets of random "belief statements" (e.g. "All zugs are wogs", "Some wogs aren't clogs"), and then both parties exchange statements over a limited amount of time, and they either both win, or both lose, depending on whether they can both find the logically inconsistent belief statement.

Because this is how we should mentally understand real-world debate.