The elevator pitch that got me most excited about rationality is from Raising the Sanity Waterline. It only deals with epistemic rationality, which is an issue, and it, admittedly, is best fit towards people who belong to a sanity-focused minority, like atheism or something political. It was phrased with regard to religion originally, so I'll keep it this way here, but it can easily be tailored.
"What is rationality?"
Imagine you're teaching a class to deluded religious people, and you want to get them to change their mind and become atheists, but you absolutely cannot talk about religion in any way. What would you do? You'd have to go deeper than talking about religion itself. You'd have to teach your students how to think clearly and actually reevaluate their beliefs. That's (epistemic) rationality.
"Why is rationality important? Shouldn't we focus on religion first?"
By focusing on rationality itself you not only can approach religion in a non-threatening way, but you can also align yourself with other sane people who may care about economics or politics or medicine. By working together you can get their support, even though they may not care about atheism per se.
I'm trying to develop a large set of elevator pitches / elevator responses for the two major topics of LW: rationality and AI.
An elevator pitch lasts 20-60 seconds, and is not necessarily prompted by anything, or at most is prompted by something very vague like "So, I heard you talking about 'rationality'. What's that about?"
An elevator response is a 20-60 second, highly optimized response to a commonly heard sentence or idea, for example, "Science doesn't know everything."
Examples (but I hope you can improve upon them):
"So, I hear you care about rationality. What's that about?"
"Science doesn't know everything."
"But you can't expect people to act rationally. We are emotional creatures."
"But sometimes you can't wait until you have all the information you need. Sometimes you need to act right away."
"But we have to use intuition sometimes. And sometimes, my intuitions are pretty good!"
"But I'm not sure an AI can ever be conscious."
Please post your own elevator pitches and responses in the comments, and vote for your favorites!