Courtesy of a former student, here’s an interesting read from Pacific Standard about the effectiveness of counter arguments and contrary information on people’s attitudes towards their own beliefs. TL;DR: counter information makes people more likely to persist in their false beliefs:
Research by Nyhan and Reifler on what they’ve termed the “backfire effect†also suggests that the more a piece of information lowers self-worth, the less likely it is to have the desired impact. Specifically, they have found that when people are presented with corrective information that runs counter to their ideology, those who most strongly identify with the ideology will intensify their incorrect beliefs.
When conservatives read that the CBO claimed the Bush tax cuts did not increase government revenue, for example, they became more likely to believe that the tax cuts had indeed increased revenue (PDF).
In another study by Nyhan, Reifler, and Peter Ubel, politically knowledgeable Sarah Palin supporters became more likely to believe that death panels were real when they were presented with information demonstrating that death panels were a myth. The researchers’ favored explanation is that the information is so threatening it causes people to create counterarguments, even to the point that they overcompensate and become more convinced of their original view. The overall story is the same as in the self-affirmation research: When information presents a greater threat, it’s less likely to have an impact.
This naturally raises the question: are we doomed? Part of the problem, I think, is that people generally argue very badly. This is part of the point of Scott and Rob’s book: Why We Argue. See here for a post the other day. Take a look, for instance, at the following claim:
This plays out over and over in politics. The arguments that are most threatening to opponents are viewed as the strongest and cited most often. Liberals are baby-killers while conservatives won’t let women control their own body. Gun control is against the constitution, but a lack of gun control leads to innocent deaths. Each argument is game-set-match for those already partial to it, but too threatening to those who aren’t. We argue like boxers wildly throwing powerful haymakers that have no chance of landing. What if instead we threw carefully planned jabs that were weaker but stood a good chance of connecting?
I don’t have any issues with this advice. Indeed, I think it does not show that argument of the basic logical variety we endorse here doesn’t work. On the contrary, it works really well; this is just how you do it.
To rephrase the author’s advice: you’ve been arguing badly all along.  Constantly going for the knock out argument is a bad strategy primarily because it’s bad argumentation. Such moves are very likely to distort the views of the person you’re trying to convince and in so doing alienate them.  What’s better is the slow accumulation of evidence and the careful demonstration of the truth or acceptability of your beliefs.