I'm 28, and I can't recall ever having to use this excuse while believing it to be a valid response. (And I reached my grad school conclusion Seth mentions when I was about his current age.)
This may be selective memory, so I could be wrong. The closest I've come on here was when I expressed shock at Alicorn's suggestion of "Why don't you just meet women on the internet?", but I could have given an answer had not HughRistik given a thorough one shortly thereafter.
In non-argumentative contexts, when I'm trying to explain something, I'll usually say, "I could explain this, and I'm sure you're capable of understanding it, but it would take a while to explain it" -- and then of course do so if they want to and I have the time. If there are steps in the explanation I don't understand, I admit it.
If I ever appeal to experience, I give an explanation of what insight that experience gives so that my opponent will be able to identify counterarguments.
Perhaps you could count my sensitivity to noise, and how I can't explain that to someone who doesn't have the same conscious experience of noise, but I can at least explain its effect on me.
To everyone, my advice would be:
1) Your job isn't as hard as you claim.
2) If you can't explain it, that says more about your own understanding of it than its actual complexity.
3) You can probably convey more knowledge than you expect.
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."