Ah, but you're forgetting that rationality and the strength of one's argument are irrelevant. This is the 21st century. People will attack you based on whatever assumptions they make about you.

So even if you don't refute the conclusion, but merely point out the flaw in argumentation, they will assume you disagree with the conclusion and will torch you accordingly. I see soup has already demonstrated this for us.

It doesn't matter how you actually feel about leg hair on women. If you point out the logical invalidity of the justification given for it, people will assume you're a misogynist.