Ask a rhetorical question: if misandry's too petty to even compare to feminism, how could it possibly be better? The other side wants it both ways. Either misandry is trivial, in which case it loses by default, or it's serious enough to compete, in which case we judge it honestly as resentment toward half the population. And if that were truly better, then every grudge would outrank every principle, which nobody actually believes.
My opponent's aspirin analogy actually cuts my way. Feminism aims at fairness for everyone. Misandry just aims at someone. Fairness wins.