Perhaps chess was a bad example, since it's not the human that contains Deep Blue's rulebook. But this excuse is used for more than just difficult AI problems; it's used for justifying moral intuitions, research inscrutability (like I thought I would see in grad school), and professional skills (like medical diagnosis, on which fairly simple expert systems beat out real doctors, and which analysis of images actually has extremely simple algorithms doctors didn't know they were using).
In the majority of cases, it's a simple matter of refusal to do the introspection necessary to identify what it is you're actually thinking, and/or an unwillingness to take the hit to status (either because you lose your mystique or because you open yourself to scrutiny you don't feel you deserve). "You" in the general sense, of course.
To give a particularly apt example, I was a libertarian for a long time before I first encountered rational justifications for laws and taboos regarding sex. And it's because their proponents aren't doing the introspection necessary to find these more general arguments.
The very fact that people found my point on homosexuality insightful, and that Morendil had never encountered the crucial underlying issue, despite (what I find to be) a sincere commitment to understanding it, is proof that a huge class of people (on a major debate, no less), were unjustifiably appealing to this inability to explain. That needs to stop.
Mind you, I do suspect the point you raise, while valid enough to consider, is nowhere near most (intolerant) people's true rejection of homosexuality.
Agree with you that "you'll get around to my view" could often be a reflex defense disguising "I know that I'm right but I can't be bothered to examine my real reasons".
Sometimes in an argument, an older opponent might claim that perhaps as I grow older, my opinions will change, or that I'll come around on the topic. Implicit in this claim is the assumption that age or quantity of experience is a proxy for legitimate authority. In and of itself, such "life experience" is necessary for an informed rational worldview, but it is not sufficient.
The claim that more "life experience" will completely reverse an opinion indicates that the person making such a claim believes that opinions from others are based primarily on accumulating anecdotes, perhaps derived from extensive availability bias. It actually is a pretty decent assumption that other people aren't Bayesian, because for the most part, they aren't. Many can confirm this, including Haidt, Kahneman, and Tversky.
When an opponent appeals to more "life experience," it's a last resort, and it's a conversation halter. This tactic is used when an opponent is cornered. The claim is nearly an outright acknowledgment of moving to exit the realm of rational debate. Why stick to rational discourse when you can shift to trading anecdotes? It levels the playing field, because anecdotes, while Bayesian evidence, are easily abused, especially for complex moral, social, and political claims. As rhetoric, this is frustratingly effective, but it's logically rude.
Although it might be rude and rhetorically weak, it would be authoritatively appropriate for a Bayesian to be condescending to a non-Bayesian in an argument. Conversely, it can be downright maddening for a non-Bayesian to be condescending to a Bayesian, because the non-Bayesian lacks the epistemological authority to warrant such condescension. E.T. Jaynes wrote in Probability Theory about the arrogance of the uninformed, "The semiliterate on the next bar stool will tell you with absolute, arrogant assurance just how to solve the world's problems; while the scholar who has spent a lifetime studying their causes is not at all sure how to do this."