and why it works so shockingly well, boils down to reason and logic, and in a very simple way. We are not talking the math of formal logic or the need to be like Mr. Spock here.
A key is that there are a handful of strategic, (not by accident or random) fallacies that often rely on emotion and simplistic thinking. It is that simple. A well-educated populace, capable of critical thinking, with just a basic foundation of critical thinking, knowledge of fallacies and understanding of bias, (you could do that in a semester or two) would help to psychologically shield people from the very common forms of manipulation we see today and that includes advertising, (and that may be why it is not standard). It simple stands out and hits you when you have that kind of foundation.
There are movements that advocate and work to bring these disciplines into the limelight and that encourage them for school curriculum.
For instance, this fallacy applies in many ways and I think the reverse may apply also, i.e., you think something is true because of being unaware of the details or complexity of it:
personal incredulity
Because you found something difficult to understand, or are unaware of how it works, you made out like it's probably not true.
Complex subjects like biological evolution through natural selection require some amount of understanding before one is able to make an informed judgement about the subject at hand; this fallacy is usually used in place of that understanding.
Example: Kirk drew a picture of a fish and a human and with effusive disdain asked Richard if he really thought we were stupid enough to believe that a fish somehow turned into a human through just, like, random things happening over time.