Here's a puzzle that I've struggled with: I love critical rationalism, but I'm a terrible debater and negotiator. Put in the context of raising kids, if they ask "why" and end up winning the debate despite being wrong, do they get their way?
Should my own actions be dictated by anybody who happens to be a better debater than me? I hope the hell not.
What if the options at hand aren't as crystal clear as the textbook cases that tend to be cited in discussions and books, and the illusion of rationality is just that? What if debate skill is not strictly rational, or even informational, but includes an emotional component plus time pressure?
I suspect that what we consider to be "irrational" approaches, such as asserting our own authority, are in fact survival skills that reflect the limitations of rational debate.