Cyinism is political too.

Of course not directly, but even the tinyiest things can and do become political. Hand gestures, clothing, music, choice of cars, choice of food, choice of words.

How is it cynical to demonstrate that a specific claim -- put across with unreasonable certitude -- is in fact flatly false?

Let me ask you: is De Morgan's theorem political? Directly? Indirectly?

Would it benefit some group more than the other? Then it has political consequences.

Logic seems fairly apolitical, but logicians rarely. Thus it's pretty reasonable to think of circumstances where simply stating a fact turns out to be political.

"Would [De Morgan's theorem] benefit some group more than the other?"

Your actual publicly adopted opinion reads like a joke.