Arguing with one is what keeps it alive. Every counter-argument is a reply, and a reply is attention, and attention is the only thing it eats.
Nobody feels obliged to debate a cold caller about the merits of boiler cover. You don't win that conversation, you simply don't have it, and the not-having takes about a second and no strength at all.
Leaving a thought unanswered is not the same as agreeing with it. That's the part that trips people up: the silence feels like concession, so they engage, and forty minutes later they're still in there. Let it sit unaddressed. It has a shorter attention span than you do.