I also said it was a fools errand - something that had little chance of succeeding against the waves of misinformation on Twitter. And finally, you’re right that knowing you can be wrong and challenging your own beliefs is fundamental to critical thinking.
It's not even about critical thinking skills. The 'other side' is often starting with a completely different set of facts. The only difference being which ones were highlighted and which were omitted.
This doesn't even touch on straight up falsities yet.
Until the sides can agree on some base first principles, it's going to be a hard problem to solve.
This point cannot be emphasized enough. I have encountered people on the opposing side of an issue who have stronger critical thinking skills than people who I agree with (and probably even myself). The differences come about due to a differences in the foundations of our knowledge or on pivotal points where neither side can claim to have an definitive answer.
If one person's POV is that <institution> should help while the other person's is that <institution> can only hurt, then they are never going to agree no matter how many links and memes and snarky comebacks they throw at each other.
You see this a lot on Hacker News too, like when the discussion touches anything related to moderation, community standards/guidelines, censorship, fact-checking, etc. A particularly popular viewpoint around here seems to be that the government (or sometimes, any powerful corporation) cannot possibly be allowed to be involved in determining the validity of any claim, particularly if that claim is controversial, i.e. there are prominent people on both sides who appear to feel strongly about the claim.
If an anonymous stranger comes to me with "Let me tell you that how you think is wrong" - yea, I don't think I'm going to buy that.
(Not that this is ever successful in places like Twitter.)
It is still a matter of trust. Approach me with respect and I'll consider your POF. Approach me with "Your reasoning process is flawed beyond your understanding" and really - who the heck are you? In the anonymity of the internet you could be anyone.
The whole thing is philosophically weird, but practically speaking, one can somewhat know that people saying aliens built the pyramids are the ones lacking critical thinking. For example, I don’t think people promoting the cancel culture lack critical thinking, even though I’d bet on it being a long-term disaster. But most anti-vaccers are pretty obviously lacking some critical thinking skills.
It’s generally the ability to tell your political interests apart from your epistemic knowledge. In simpler terms, the ability to engage less in wishful thinking. While perfection is impossible, I do think it’s possible to improve in this ability. Proving it to others is another challenge; You probably need to predict counterintuitive results consistently for people to somewhat trust in you.
Critical thinking is a skill that is almost useless to most people and can lead to being a net negative. It's the skill of critique. One can be amazing at critical thinking and be absurdly terrible at constructive thinking. Politics in general needs far less critique and far more construction. It's really bad to get people very aware of just how badly they're exploited but then to give them no potential solutions to solve it. That's basically what wokism has done recently. Every solution proposed by them is so unpalatable to the rest of the nation that there is no place for constructing new policies.
The left has this problem especially bad since the radical left makes being really good at critique a whole component of their intellectual tradition:
Everyone everywhere on the internet thinks that the "other side" lacks critical thinking skills. I'm not surprised your effort failed, I'm sure if you offered to teach me critical thinking skills I'd wonder who the heck you thought you were.
Frankly your confidence in your own impeccable critical thinking skills cast doubts. The smartest people are those who know they can be deceived. If you don't have the humility to check your own reasoning then you are probably wrong about something.