Andy Norman, a philosophy professer at Carnegie Mellon University, led a team to create a game called Socrates Jones: Pro Philosopher to teach critical thinking skills. It's a serious yet fun exercise in learning how to spot weak arguments and challenge shaky claims.
Yet, demanding that a person follow your personally-approved-of restrictions on what can be said, and why, before you'll bother listening is also a common silencing tactic, and it's particularly effective when employed by the entire status quo. You can tack on all sorts of arbitrary restrictions and make it sound like you're formalizing the discussion when your true goal is to stop people with different world views than yours from airing their points.
Jester: How many responsible, mature adults does it take to screw in a light bulb?
Responsible Mature Adult: This is not a constructive conversation. (leaves room)
If you wanted to have a rational, constructive discussion on gun control, for instance, you might keep things civil by excluding anyone who owns one, since they're obviously going to give predictable, tired anti-control arguments. And you'd exclude anyone who's been robbed at gunpoint since they're obviously going to be emotionally biased and make judgements based on personal preference rather than the Greater Good. You'd certainly exclude anyone who uses poor terminology. Anyone who calls a magazine a "clip" clearly doesn't understand the topic well enough to be worth listening to, and as for people who use the very word "gun" instead of "firearm", well…. "Gun" is both ambiguous (a pistol is a gun, but so are a Howitzer and a cannon on a pirate ship) and laden with negative emotional overtones. If a person says she desires a constructive, rational, intelligent discussion, but then uses poorly-defined, emotionally distracting words, she's either woefully unprepared to deliver on her promise or she's lying as to her true intent. Either way, she doesn't belong in that talk, now, does she?
Critical thinking isn't for determining who's right. It's for determining who has a valid argument. It's great for answering, "Who should I listen to?", but that's not equivalent to "Who knows the truth?" It's only a good approximation. There is always the Fallacy Fallacy to consider. Using a poor argument doesn't make you wrong, just unconvincing.