It would go over:
1. Rhetoric
2. Historical methods of propaganda
3. How propaganda spreads
4. "Virality in communication networks" (https://www.amazon.com/Hooked-How-Build-Habit-Forming-Produc...)
5. Gossip
6. Tactics of Manipulation (48 laws of power is a good recording of this)
7. Strategizing on cognitive basis.
Nobody wants to explain to their 5yo why they can't afford a Barbie Jeep but can afford booze or going out to eat. Nobody wants a teenager that is well versed in assessing the goals and motivation of all the parties in any given situation because they'll recognize all the partial truths they get fed in an attempt to make them to take risks in a manner more like an adult. A teenager that understands statistics well would be impossible to scare into not doing "bad things". Likewise thinking critically is not a high priority thing for parents to teach.
When you're dealing with someone who can't think on the same level as you lying is just so damn easy. They are playing checkers. You are playing seven dimensional chess. Teaching kids to think critically requires a constant effort and directly negatively impacts the parents in the short term. It's like quitting smoking for 18yr, no wonder most people don't do it.
Then, start asking questions: can we trust the information we receive? Is it possible we receive a biased/incomplete/wrong information? Are we being manipulated? Who would benefit from supplying us with incorrect information? correct information? How can we verify the information?
Look at the history. What can we learn from historical events? Have we been lied to in the past? How did we learn that we've been lied to? Who benefitted?