For instance, it is intuitive for politicians to increase their power but the point of liberal democracy is to limit power. So liberal democracy is counter-intuitive.
And for instance, the language of science is mathematics and almost all of science is counter-intuitive.
And the modern economics of Adam Smith is counter-intuitive for who, before Adam Smith, would have thought intuitively that private greed leads to public prosperity.
Yes, most of the modern world is based on universal literacy and so most of the modern world is counter-intuitive.
However the modern world based on universal literacy is coming to an end and we are entering the noosphere based on electronic media.
But we still drive forward looking in the counter-intuitive rear vision mirror of literacy instead of looking through the intuitive windscreen of the electronic media, the noosphere.