I'm not who you were replying to but I think what people typically mean is instead of just being told X is true you help people come to the conclusion that X is true. One of the best way to do that is to understand both sides of an issue and come to the conclusion that one side is correct. Not only does it cause people to understand why they believe something but it causes them to understand why people on the opposite side of this topic believes what they do.
Many people are guilty of not actually understanding why people believe what they do. They will read arguments by people on their side but won't read the best arguments made by the opposite side. They will instead read the arguments by either people who make crappy arguments or by people on their own side explaining the opposition's view. This typically results in awful, often strawmen arguments for the opponent's views.
If teachers could set up debates between students on topics I think it would be good. Ideally, the student should disagree with the side they are supposed to defend, though isn't always possible. This will force them to look up the views held by the other side. The teacher should understand the best arguments on both sides and should step in when arguments are being made incorrectly or when a student misses a good response.
This of course would often times not work well because teachers don't understand their opponent's views so I am not sure how to actually handle this. You could possibly have a teacher with a different view help moderate the debate, but there is a disproportionate amount of teachers who are liberal (I've seen some studies that put it at over 80%) so it would not always be practical.
This doesn't always work on every topic like math, but it could be helpful in both English (for meaning behind books, poems, etc) and various history topics.
I am sure there are additional ways to help students learn critical thinking but this could be a good way if teachers are actually able to present both sides in a fair way.