Wise Old Owl
There is definitely a connection between wisdom and limiting what we say. Proverbs 10:19 says, "In the multitude of words sin is not lacking, but he who restrains his lips is wise."
We are wise to be very careful about what we say or how much we say in certain situations. It make perfect sense to be careful of our words when we a somewhat angry about something. Although there is a time to be quiet and a time to speak, choosing to speak less allows us to hear more.
There's an expression that goes like this: A wise old owl sat in an oak; The more he saw the less he spoke; The less he spoke the more he heard; Why can't we all be like that wise old owl?