I think your somewhat mistaken. Applying a reasonably measured pain through disciplined correction is what the Bible is referring to and its a sign of love. Children don’t have their full faculty of reasoning abilities quite formed in the early years. Perhaps AP went overboard with it__ I cant say.
John Gill:
“Verse 24
He that spareth his rod hateth his son,.... Who withholds or withdraws his rod of correction, which is in his hand, which he has power to use, and ought to exercise at proper times; he, instead of loving his son, may be said to hate him; for such fond love is no better than hatred; and, if he really hated him, he could scarcely do a more ill thing by him than not to correct him for a fault; which was the sin of good old Eli, and both he and his sons suffered for it;
but he that loveth him; that has a true love for his son, and a hearty concern for his welfare and future good; he will regulate his affections by his judgment, and not give way to a fond passion, to the prejudice of his child: but he
chasteneth him betimes, or “in the morning”F24; in the morning of his infancy, before vicious habits are contracted, or he is accustomed to sinning, and hardened in it; or as soon as a crime is perpetrated, before it is forgot or repeated: or every morning, as Jarchi and Aben Ezra; that is, continually, as often as it is necessary, or as faults are committed.”