Quick answer
Three lines, three tools, and the third is deliberately jarring. The saying observes that some creatures respond only to physical restraint and places the fool in that company.
Read both lines
The rhetoric works by list. Two animals with their standard equipment, then a man, and the reader is meant to feel the insult of the arrangement. That is the point: the fool has put himself in a category he should not be in, and the saying's contempt is for his refusal to be reached any other way.
Notice that this is an observation about an adult in an ancient legal setting, where corporal punishment was the ordinary civil penalty, and the same collection puts judicial beatings at 19:29 and the threshing wheel at 20:26. The verse is describing what the world does with a certain kind of man, not prescribing a method to anyone.
What it does not mean
This is not a license to hit anyone. It is not about children, and it must not be pulled into the formation complex at 13:24, 19:18 and 23:13–14, which are about a parent and a child and carry their own explicit limit. It is not permission to strike an adult, a spouse, or a person under your authority. The catalog's standing rule applies with full force here: a verse about a type may never be used to dismiss a person, and this one has more capacity for harm than most.
What the saying actually observes is bleak rather than instructive. Some people will not be reached by words, and the book says so at 27:22, where grinding a fool in a mortar leaves his foolishness intact. That is a lament about the limits of correction, not a recommendation of the mortar.
Related: Proverbs 27:22 · Proverbs 19:29 · Proverbs 10:13 · Proverbs 17:10
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.