I don’t like that phrase.
There’s nothing wrong with the spirit behind it, really. Claims that contradict your existing model of the world should require more evidence than your existing model has before you believe them. But that’s not how it gets used. It gets used to mean “your claim sounds absurd to me so I choose not to believe it”.
Now, in day-to-day life, your absurdity heuristic works just fine, which is probably why you have one. But when you’re trying to have an argument with someone, I think that’s a thing you should suspend until the argument is over, because it’s annoying and almost never useful. Arguments are about comparing evidence. “Your claim is absurd!” isn’t evidence, it’s your system-1 doing its best to react to evidence. And I don’t think you trust your system-1 to be rational enough that you should take its word as evidence of anything. “Einstein said so” is probably some evidence in your favor, in an argument about physics. “My intuition said so” is not.
It gets especially bad when Person 1 yells “Extraordinary claims require extraordinary evidence!” in an argument about whether the claim does, in fact, contradict established theory, which is what most such arguments are about anyway. Yelling that phrase when someone claims relativity is false? Sure. Yelling it when they claim that many-worlds is the correct interpretation of quantum mechanics? No.
(Disclaimer: I know very little about quantum mechanics and I certainly have no stance on what interpretation is correct, it was an example.)
