I agree that your interlocutor is being ridiculous. But the analogy doesn't hold because your interlocutor doesn't have any reason to disagree with your statem

I agree that your interlocutor is being ridiculous. But the analogy doesn't hold because your interlocutor doesn't have any reason to disagree with your statement; they're just being a troll. In any case, someone might rationally object to any such analogies because they disagree that there is an equivalence between names and pronouns.