This proverb is just common sense. Both responses are seemingly in answer to something said inappropriately. A gentle response could diffuse a tense situation, but a harsh response will simply escalate things from bad to worse.
Sad to say, many of us guys think that soft words are not very manly. When we feel like someone has disrespected us, we tend to feel our manhood is being challenged and we need to respond in kind. “I’m a grown-a_ _ man and you can’t talk to me that way!” is an all-too-common response.
But results are clear – if I want to stir things up, just respond in kind. If I want to get out of this unpleasant situation – a gentle answer will do just fine.