We all know confidently incorrect people. People displaying dunning-kruger. The majority of those people have low education and without someone giving them objectively true feedback on their opinions through their developmental years, they start to believe everything they think is true even without evidence.
Memorizing facts, dates, and formulas aren’t what necessarily makes someone intelligent. It’s the ability to second guess yourself and have an appropriate amount of confidence relative to your knowledge that is a sign of intelligence.
I could be wrong though.
There’s a lot of different things that get pumped into “intelligence”. There’s “reasoning ability”, “knowledge”, “wisdom”, and a whole host of others, some in the category of traditional intelligence, and others around things like emotional intelligence.
Raw knowledge is something that schools can teach through memorization. You have facts. Memorization isn’t the best way to do it, since context and such can often make information stick better, but some things you’re eventually going to memorize, intentionally or not (I don’t calculate 6*6=36 every time).
Reasoning or analytical ability is much harder to teach, since you can’t really make someone more able to have insights and such.
Wisdom is something that can be trained I’d phrase it. I don’t think you can be taught it like you can a history lesson, but it needs to be trained like a sport. How to apply reason to a situation, how the knowledge you have relates to things and other bits of knowledge. Which things are important and which aren’t.
It sounds like you’re mostly taking what I’ve called wisdom, with a dash if introspection tossed in, which can play very well with wisdom. “How sure am I about this?” Is a question wisdom might make you ask , and you need to know yourself to know the answer.
Knowing how to question the right part of something, so that you’re not getting caught up in the little inconsistencies and missing the big one, or considering the wrong facts that are unimportant to a situation.
(A pet peeve of mine) Sometimes people will bring up statistics of race in relation to crime. People with perfectly good reasoning ability and knowledge will get caught up debating the veracity of the statistics, or the minutiae of the implications of how other statistics interplay to lead to those numbers, both in an attempt to deny the conclusion of the original argument.
The more wise thing to do is to question why this person is making the argument in the first place. Use your knowledge of society to know there are racists who want to convince others. Your reasoning to know that someone more interested in persuasion than truth can twist numbers how they want. Reject their position entirely, instead of accepting their position as valid and arguing their facts.