when I say "what's the evidence for that?", it's not that I don't trust your rationality (although of course I don't trust your rationality either), but I just can't deduce what evidence you must have observed from your probability declaration alone even if you were fully rational.

Yes. There are reasons to ask for evidence that have nothing to do with disrespect.

• Even assuming that all parties are perfectly rational and that any disagreement must stem from differing information, it is not always obvious which party has better relevant information. Sharing evidence can clarify whether you know something that I don't, or vice versa.

• Information is a good thing; it refines one's model of the world. Even if you are correct and I am wrong, asking for evidence has the potential to add your information to my model of the world. This is preferable to just taking your word for the conclusion, because that information may well be relevant to more decisions than the topic at hand.