That's called Reductio Ad Absurdum and is a valid, classic form of argumentation. If you take their premises to their logical conclusion, the result is absurd, so their premises must be false.

You don't get to arbitrarily limit where a premise gets applied in order to pick and choose which conclusions to stand by. It isn't a strawman to show that someone's premises lead to conclusions that they would disagree with, that's literally the point.