John Gill Commentary Proverbs 26:3

"A whip for the horse, a bridle for the ass, And a rod for the back of fools." — Proverbs 26:3 (ASV)

A whip for the horse
One that is dull of going, or refractory and needs breaking; a bridle for the ass ;
not to curb and restrain it from going too fast, asses being generally dull; but to direct its way and turn it when necessary, it being stiff-necked and obstinate; though the Septuagint, Syriac, and Arabic versions, render it a "spear" or "goad", something to prick with, and excite it to motion; and so the Targum; or otherwise one would have thought the whip was fitter for the ass and the bridle for the horse.

and a rod for the fool's back ;
suggesting that the fool, or wicked man, is like the horse or the mule; though not without understanding of things natural, yet of things divine and moral; and as stupid as the ass, however wise he may conceit himself to be, being born like a wild ass's colt; and instead of honour being given him, stripes should be laid upon him; he should be reproved sharply, and corrected for his wickedness, especially the causeless curser, (Proverbs 19:29) .