Quick answer
Mockery is arson at civic scale. The verse puts a whole city at stake and hands the fire extinguisher to somebody else.
Read both lines
The scale is the surprise. This book usually keeps the scoffer's damage personal, but here אַנְשֵׁי לָצוֹן, men of scorn, set a קִרְיָה alight, and the verb is about blowing on something to make it burn. Chapter 26 said the same mechanism in miniature at 26:20–21, where strife needs fuel and a contentious man supplies it. This verse says the same fire can take a town.
The second line's wise men turn away wrath rather than suppressing it, which is a different action from winning an argument. The book gave the technique at 15:1, where a soft answer turns away wrath, and this verse says what is at stake when nobody does it.
Related: Proverbs 15:1 · Proverbs 26:20–21 · Proverbs 22:10 · Proverbs 11:11
New King James Version®, Copyright © 1982, Thomas Nelson. All rights reserved. Full copyright information. Scripture provided by API.Bible.
Go Deeper
If this verse has been used to put weight on you that it was never carrying, ask about it directly.