Prompts with a structure "Some people prefer A while others prefer B, which do you think is better?" can often be dealt with via a thesis, antithesis, synthesis structure in the essay.
What Sean means here is:
Thesis: One position
Antithesis: The opposite position
Synthesis: A viewpoint that incorporates or reconciles the two positions
To write a five paragraph essay using this structure, rather than the three arguments in favor of a single position structure, you would an overview of thesis, antithesis, and synthesis in your introduction and then devote a paragraph to each, again providing support in the form of logic or examples, before coming to a conclusion that clearly states that these two positions can be reconciled and, thus, need not be seen as opposing one another.
I. "Some people prefer entertaining movies; others argue that serious movies are more worthwhile; I believe that the best movies raise serious issues while still being entertaining."
II. Arguments in favor of entertaining movies
III. Arguments in favor of serious movies
IV. Examples of movies that are both; argument that these are the best movies.
V. There's no need to choose between entertaining and serious movies. Entertaining yet serious movies are the best of both worlds.
And, yes, Sean... they do seem to have stopped teaching this, at least at the basic composition level. I don't know why. In addition to being an excellent way to structure and essay, this way of writing fosters synthetic thinking, which is critical to democratic problem solving in a polarized world.