Why would he/she need evidence? It's an observation which you may disagree with. Asking him/her to provide evidence is just silly. He/she is not here to prove anything to you.
The idea that observations “contain evidence” is an idea that I’m unfamiliar with. I’m not sure what point you’re making about observations or assertions, or how the distinction between the terms is germane (not talking about the distinction between the concepts).
Asking for evidence is confrontational and a bit gauche. Better to ask someone to elaborate, or ask them what the reasoning is. That’s a good way to continue the discussion because it doesn’t frame the discussion as an argument.
It's germane because the OP (and you) seem to think it's inappropriate to ask if you have any examples (maybe "example" would have been less "gauche" than "evidence")
It's not really important, you've clarified, and even added in some advice on manners.