In that case, we can replace “point out where in their argument they went wrong” with “point out where our underlying value judgments seem to diverge.”
If they then try to argue that your values are wrong and theirs are right, either you have to move the discussion up a meta-level or, yes, screaming.
Maybe they didn’t go wrong, and there is no paradox, and it is a matter of relative values as to which is more important.
In which case screaming makes a lot of sense as a strategy.
In that case, we can replace “point out where in their argument they went wrong” with “point out where our underlying value judgments seem to diverge.”
If they then try to argue that your values are wrong and theirs are right, either you have to move the discussion up a meta-level or, yes, screaming.