Quick answer
Walking away is the achievement. Starting a fight takes no skill at all, which is the second line's whole point.
Read both lines
Honor is the word to watch, because the ancient world located it in winning and this verse relocates it in stopping. The first line describes a man ceasing from a dispute that is already underway, so this is not conflict avoidance but disengagement mid-argument, which costs more. Then the second line removes the prestige from the alternative in the plainest way available: any fool can do that. It is not an insult so much as a deflation. The book has been building this since it made patience a function of insight at 19:11, and 17:14 gives the reason to stop early, since the beginning of strife is like releasing water.
Related: Proverbs 17:14 · Proverbs 19:11 · Proverbs 26:17
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.