"One who spares the rod hates his son" (13:24). Why does the saying speak of hate and love?

The saying has two halves: "One who spares the rod hates his son, but one who loves him is careful to discipline him" (13:24). It sets hates against loves, and spares the rod against is careful to discipline him. Discipline is musar, the word of the son's "father’s instruction" (13:1) and of "refuses discipline" (13:18) (tap instruction). Is careful is shachar, the verb of Wisdom's "Those who seek me diligently will find me" (Proverbs 8:17), and Brown-Driver-Briggs gives this verse's words as "seeks him early (with) discipline" (tap careful). Proverbs 3 sets love beside correction too, of the LORD: "for whom the LORD loves, he corrects, even as a father reproves the son in whom he delights" (Proverbs 3:12). The book speaks of the rod again (Proverbs 22:15, 23:13-14, 29:15). These notes explain 13:24 only from its own words; they don't apply it to any modern practice, law or debate, or say how anyone should discipline a child. If this saying touches anyone harmed at home, make room to talk, and help them find someone they trust to talk to further, such as a pastor or a counselor.