If you say nothing at all, then you can't say anything embarrassing or inappropriate. A play on the idiom "put (one's) foot in (one's) mouth" (to say something stupid). A: "Oh my god, I can't believe I said that. Why are you being so quiet?" B: "Because a closed mouth gathers no feet!" Knowing that I would inevitably say something ridiculous, I kept my mouth shut—a closed mouth gathers no feet, after all.