Wrong and liberal, for that is only one use of the word shêbeṭ, , while it basically means to
to branch off; a scion, i.e. (literally) a stick (for punishing, writing, fighting, ruling, walking, etc.) or (figuratively) a clan:—× correction, dart, rod, sceptre, staff, tribe. - Strong's, H7626 )
And thus it often speaks of an instrument used by authority, including in discipline, the very thing you deny!
And if a man smite his servant, or his maid, with a rod , H7626 and he die under his hand; he shall be surely punished. - Exo 21:20
He did not smite the slave with a mere claim of authority, but an instrument used by authority.
John Gill provides some insight from Jewish commentary (for what its worth):
Exodus 21:20: And if a man smite his servant or his maid with a rod,.... A Canaanitish servant or maid, as the Targum of Jonathan, and so Jarchi; and that only with a rod for the correction of them, and not with a sword or any such destroying weapon, which would seem as though he intended to kill, yet nevertheless:
and he die under his hand; immediately, while he is smiting or beating him or her, on the same day, as the above Targum interprets it:
he shall be surely punished; or condemned to the punishment of being slain with the sword, as the said Targum and Jarchi explain it: this law was made to deter masters from using severity and cruelty towards their servants.
2Sa 7:14: I will be his father, and he shall be my son. If he commit iniquity, I will chasten him with the rod H7626 of men, and with the stripes of the children of men:
God is not chastening by the authority itself, but with instrumentation of it.
Psa 23:4 Yea, though I walk through the valley of the shadow of death, I will fear no evil: for thou art with me; thy rod H7626 and thy staff they comfort me.
Phillip Keller in "A Shepherd Looks At Psalm 23" relates ,
Each shepherd boy, from the time he first starts to tend his father's flock, takes special pride in the selection of a rod and staff exactly suited to his own size and strength...The rod was what he relied on to safeguard both himself and his flock in danger. And it was, furthermore, the instrument he used to discipline and correct any wayward sheep that insisted on wandering away...If the shepherd saw a sheep wandering away from its own, or approaching poisonous weeds, or getting too close to danger of one sort or another, the club would go whistling through the air to send the wayward animal scurrying back to the bunch...Finally the shepherd's rod is an instrument of protection both for himself and his sheep when they are in danger. It is used both as a defense and a deterrent against anything that would attack. ...
Pro 10:13: In the lips of him that hath understanding wisdom is found: but a rod H7626 is for the back of him that is void of understanding.
Obviously the rod is a a literal instrument and used for correction, and thus it may also refer to what authority can do by other means of correction.
Pro 13:24: He that spareth his rod H7626 hateth his son: but he that loveth him chasteneth him betimes.
The literal rod is used for chastening, and to not use it if and as needed is actually hateful in effect, despite the emotion involved.
Pro 22:15: Foolishness is bound in the heart of a child; but the rod H7626 of correction shall drive it far from him.
Thus the rod represents physical chastisement.
Pro 23:13,14 Withhold not correction from the child: for if thou beatest him with the rod , H7626 he shall not die. Thou shalt beat him with the rod , H7626 and shalt deliver his soul from hell.
Once again obviously the rod is a a literal instrument and used for correction.
Pro 26:3 A whip for the horse, a bridle for the ass, and a rod H7626 for the fool's back.
Thus the rod is like a whip for the horse,
Pro 29:15 The rod H7626 and reproof give wisdom: but a child left to himself bringeth his mother to shame.
Thus the just and wise use of physicality correction is part of wise Scriptural child rearing of the wise, while fools despise such correction.
There’s also the word translated “smite” in Exodus 21:40, which is Hebrew “nakah”; it unambiguously refers to a physical blow, that can create physical wounds that vary in severity according to how hard the “nakah” is, even (as the verse noted) a killing blow.
Typo: Exodus 21:20.
Allow me to add this detail to your discourse on The Rod:
The topic under consideration is "spanking." which I believe means striking with the open hand. In actuality, that is not the method the instruction of Scripture leads us to, which is the application of the rod, not the open hand. To wit, spanking is actually sparing the foolish child (or childish fool) from the God-ordained instrument of chastening, the rod; and thus causes the child to think that he/she is hated (or at least, 'loved less' as some would have it), rather than chastened with his benefit in mind.
Now in fact, I did not spank my children. I used the instrument that my mother employed, the leather belt, a strap, which would be a form of whip, but not in excess--only to the point where it was clear that the lesson had been learned. (I used a broad one, and that with only three strokes. It was never used on a child after the twelfth birthday.)
However, when my son grew up and had taken unto himself a godly wife, they taught me that the rod, not the hand or a whip, was the God-given instrument to be used, even for a tiny babe desiring to exert his/her will against the parent's!
So, how big and hurtful should the rod be, to begin to discipline the infant?
Well, when the baby (who was being breast-fed on a set schedule) started agitating at the wrong time of day or night, and cold not be hushed up by soothing, a soda straw was produced, shown and seen, then applied to the open skin of the babe's arm or leg to show displeasure. Then the babe was tucked back in with a goodnight kiss but without any reward of feeding at all. If the agitation began again after this quieting, the process was repeated. The babe soon learned that he/she was not the dictator, and that starvation, recreational feeding, or deprivation of affection was not a part of the lesson of establishing authority.
This, of course, lays the groundwork for the pattern of dealing with other behavioral issues as they occur in the child's growth and responsibility for self-control.
When the child was older and the straw-sign was too mild, a firmer instrument was cut from the longest straight part of a plastic (not wire) coat hanger, and used in the same way, but was applied until, and only until, the child's defiance crumbled, a quiet, lasting resolutiond be made, and assurances of love extended. The rod was of a size to fit in Mom's purse, such that when in public the child was causing Mom to reach inside for it, usually that was enough to bring restraint.
Speaking to the threat of an observer calling Child Protective Services, the complaining interloper would have a hard time explaining that any abuse was taking place, whereas a cuff or slap or quick kick accompanied by an angry remonstrance might be actionable.
In the end, though when his children were old enough to graduate to a half-inch hardwood dowel with my son administering it, it never had to be used, as far as I know. And so he and his dear wife have raised ten children, the youngest now turning eight, and the oldest this year finalizing his Ph. D. in Mechanical engineering. His sisters have gone on several missionary trips with one remaining in the field at a Costa Rican orphanage. His younger brother received his Army ROTC commission this spring and is now on active duty. All the other children continue to honor their father, their mother, and their home education with responsible behavior and self respect. My perception is that this is a commendation for the use of the rod of correction as an absolutely necessary part of the task of raising self-governing reliable citizens; that to fail in this is a deliberate "cop out.".
When as a child I visited my grandpa and grandma farmers, it only took a couple of times for grandpa to take down the razor strap hanging on the back of the bathroom door, double it, then snap it together with a loud pop for me to gain the clear impression that when he issued a request, he was not starting a debate about it. That's the way my Dad was raised, and very effectually induced me to follow the same pattern.
But it's the rod that works, when applied until resistance to properly instituted authority ceases, and remains that way as a fixed principle.
As a final comment: No spanking. It is not a God-given method for chastening, and it is a process not formidable enough to cause deep-rooted character to be formed in the trainee.