I am reasonably intelligent. I am interested in the topic, and so am well read and informed. My conclusions follow reasoned lines, match presented evidence well, and are rationally the most likely. They are scientific. Many other interested and intelligent people have also come to the same conclusions.
You, however, disagree. How can this be? Since my conclusions are rational and informed, you must be biased by your ideology, your vested interests. You must be selectively ignoring key evidence: denying the science. You must therefore be ‘anti-science’. Maybe you have been persuaded by ‘misinformation’ distributed by vested interests and lobbyists, using tried and tested techniques to appeal to your emotions rather than reason. Or maybe you just lack the mental skills to be able to properly assess the complexities and uncertainties.
Convinced? No? Then it must be because one ‘cannot reason someone out of a belief they did not reason themselves into’. I am still the rational, correct one, and you are, basically, unreasonable.
This inability to understand, assess, value and maybe even argue convincingly for wide-spread opinion that we disagree with is sign of intellectual weakness in an argument. It suggests ideologically-based bias: we have been too narrowly selective about the ways in which we assess the facts, the reasons and the effects. Can those of us interested in these things make good cases for both evolution and creationism? For homoeopathy? Both for and against late term abortion? Any abortion? For cake? Smoking in pubs? Permitting a new local Tesco’s? How much fruit and veg we ‘should’ eat? And for what?
If we cannot understand and adjust the priorities assigned to evidence and reason that forms the conclusions that many other people hold, then we probably haven’t understood the problem properly. Even if later, with hindsight, we find we have come to the ‘correct’ conclusion, it is likely by accident or social identity, not reason.
This is not about persuading or convincing, or about getting inside the heads of people you disagree with in order to change their mind. It’s about better understanding the problems and their associated issues, and so coming to conclusions that better usefully match the real world.