In the past, intellectual people believed that due to the large number of illiterate people, there are no readers and followers of philosophers and scientists, and they were betting on imposing compulsory education on people to change the equation. However, the reality has refuted that hypothesis and proved that despite the continuous increase in the number of educated people, superficial discourse is still the favorite discourse for the vast majority of people.
That's an interesting research topic. My guess is that most people have limited exposure to scientific and logical discourse, and so it becomes hard work for them to process it. It's up to us to summarize our arguments in language that can be understood by all.
Although nowadays people are more educated than in the past, even most educated people feel more at ease with light discourse most of the times, but it obviously depends on what kind and what level of science or philosophy is concerned.
Actually, to add to my previous answer, one of my professional organizations sees this as important enough to warrant a workshop:
Professional Development Workshops – Association for Psychological Science – APS: Science communication: Engaging non-scientists
This is a nice question. I have three points in my answer:
1. What you refer is analytic discourse, and it usually has less training and teaching. The mainstream in primary, secondary and higher education, does not use it. Therefore, most of the people does not have enough educational opportunity to learn it, even though they received more years of education.
2. To learn about science is to learn scientific thinking, that usually challenges our most frequent ways of reasoning. That is a lucid conclusion given by Stellan Ohlsson, a rearcher on learning in school settings, and what Gaston Bachellard, a French physic and philosopher of science, had in mind when he explained his concept of "epistemological obstacle".
3. Advances in education access does not eliminate differences and opportunities in the type of knowledge and discourse used actively by people in function of their social class. People receive some discourse in school, but they elaborate also discouse received through other environments and social bonds and interactions. Important sociologists elaborated explanation in that line, like Pierre Bourdieu (French), Basil Bernstein (British), and Peter Balu and Otis Duncan (Americans).
A very topical, though I would say almost intractable problem. One thing to look into might be the 'Dunning-Kruger Effect' - where people over-estimate their own knowledge and insights and seem impervious to any other information. See, for example, this: https://quod.lib.umich.edu/e/ergo/12405314.0004.010/--bullshitting-lying-and-indifference-toward-truth
Berstrom & West's Calling Bullshit: The Art of Skepticism in a Data-Driven World might also be useful to look at.
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