I honestly think that the practice of demanding a source or a claim is instantly invalid is a bad one. If I make a claim, it's because at some point I wanted to know the answer to something, so I looked it up. Or, I didn't believe a claim someone else made.
It's a mistake to trust some stranger on the internet to provide an unbiased source that wasn't cherry picked to support their position.
Plus, most sources can be found with a <5 word Google search.
Sometimes it just works to insist you did the work.. I say I looked into <> extensively and that's what I found. Feel free to come back later and present me with evidence to the contrary.
And (this is the crucial part) I just don't accept any further argument in that moment.
Honestly this worked so many times. Like barely anybody ever came back to me another day but at the very least I got them to shut up in the moment.