I did this in high school, in something called Lincoln-Douglas debate. It dealt mainly with moral issues, like abortion, capital punishment, euthanasia and the like. You would do three debates, and had to do both sides. You would alternate between defending a proposition, and attacking it. If your task was to support, say “Resolved: that abortion is inherently immoral and should be made illegal again”, you were on the Affirmative side. If you opposed it, you were Negative (or so I recall). A speaks 5 minutes, say, then is cross examined by N. N then speaks 8 minutes, then is cross examined by A. A then gets the final 3 minutes. Something like that. If you did A the first round, you did N the second, and A the third. Since A got the last word, most people preferred it.
To win, you need to clearly define your terms. “Abortion” for example, could as one rhetorical method be confined to any killing of fetuses that are older than, say 6 months. You could call it infanticide, and note the general historical cultural rejection of infanticide. You would need to define immoral (Golden Rule, Categorical Imperative, Christian teaching: the choice is yours. I tended to use Kant and Rousseau), and define illegal–such as HOW illegal (felony, misdemeanor), illegal for who (doctor, pregnant woman, helpers), and under what jurisdiction (Federal, State, City, County).
And you need criteria by which to judge the claims. Obviously, getting the judges to accept your criteria then showing how your case best fits those criteria is the way to win. Obviously, you will have two opposed ways of looking at it. You may have one person making a narrow claim, and the other claiming everything else, or two people fighting it out for the middle. Many things are possible, and many approaches are possible.
But you need something like, say: “Murder is inherently immoral”. You then perform a logical operation, such as: Abortion constitutes a murder. Therefore abortion is immoral.
The negative, say, on this one, will be to define murder as the killing of a human person who is breathing and viable.
But overall, and over time, you learn to think in terms of principles, and you learn to value the use of clear language. You learn to see the merits of both sides in complex questions like these.
And obviously politically, it would be useful to do survey courses such as “modern political theories” where students learn in detail what conservatives think and why, and what leftists of all varieties think and why. They could read, say, “Conscience of a Conservative”, and Edmund Burke, and John Stuart Mill. They could read Hayek and perhaps even Ayn Rand. Then they could read whatever else the teacher sees fit.
And at the end of the semester they could have a debate tournament, with the top five finishers guaranteed an A in the class, where they debate a political question from both a conservative and a leftist point of view. If there are any conservatives, they get to see things from a leftist perspective, and vastly more importantly, the many leftists at least learn to use the words, principles, and ideas of conservatives in a way which is not cartoonish and highly prejudicial.