What would it mean when an ideologies arguments can't be taken seriously unless you're sure the speaker is sincere?

Well... OK, consider the following distinct but related pattern.

I do in fact believe that the reason the government ought, as a rule, not take infant children away from their parents and feed them to baby-eating aliens is that the consequences of doing so would probably be negative. But if someone were to nod their head in my direction at a party and say, in a conversation, "Of course Dave here probably thinks the reason the government shouldn't kidnap my babies and feed them to aliens is because the consequences of doing so would probably be negative," I would conclude I was being ridiculed. (I would probably conclude that I was being playfully ridiculed, aka "teased", rather than seriously ridiculed, though of course it would depend on the circumstances.)

So what does it mean when my own positions can be quoted back at me accurately in order to successfully ridicule me?