It often happens to me that someone sees me stopped and staring into space thinking as a result of what they say, and conclude that what they said was a really strong argument for their position, where what's actually happening is that they've revealed such a depth of confusion that I'm briefly lost looking where to start unpicking it.

My technique is get time is to say "wait" about ten times or until they stop and give me time to think. This probably won't work for comment threads very well, but in reality not letting the person continue generally works. Probably slightly rude, but more honest and likely less logically rude, a trade-off I can often live with.