Our purpose here is not to examine the broad issue corporal punishment in modern times, but to address one atheist's comments specifically. Critics cite passages from Proverbs like 23:13-14:
Withhold not correction from the child: for if thou beatest him with the rod, he shall not die. Thou shalt beat him with the rod, and shalt deliver his soul from hell.
Several other passages from Proverbs frequently make an appearance, as does Deut. 21:18-21. It is argued that these verses could be cited by any unreasonable parent to justify reprehensible corporal punishment.
The critical word is unreasonable. It is obviously possible for any "unreasonable" person to misuse or misapply anything, no matter how clear it is. In this particular case, any parent who uncritically applies these passages for things like Johnny not cleaning his room would not only be unreasonable, but acting without respect for the social context of these texts.
Our primary source here is Crenshaw's Education in Ancient Israel. We have lost the realization that for the ancients, education wasn't simply a matter of teaching times tables so we can get a job selling timeshares: Education was a matter of survival, of ensuring that what there was of civilization did not slip over that fine line from order into chaos.
Thus all of the Ancient Near Eastern wisdom literature is filled with pithy sayings along the lines of, "A student's back is his ear." Even as today students had to be taught to want to learn -- the only differences are that the options for distraction have become more diversified (i.e., video games, versus, i.e., trips to the prostitute's house), and most of us aren't perceptive enough to see through our society's complexity to know that chaos is just as possible here and now.
We don't see a reason to associate severity with education, but if we wait long enough and have enough school shootings and other travails, perhaps we will.
Just for context, here are parallel sayings from the time, provided by Crenshaw:
Withhold not from thy son the rod, else thou wilt not be able to save [him from wickedness]. If I smite thee, bu son, thou wilt not die, but if I leave there to thine own heart [thou wilt not live]. -- Abiqar, Saying 4
I grew into a youth at your side. You beat my back, your teaching entered my ear. -- Papyrus Lansing, a schoolbook
As Crenshaw puts it, "In the Bible, education originated with the desire for order and continuity. To combat the powerful and seductive lure of chaos in various forms, societal or personal, older and more experienced individuals tried their best to prevent the younger generation from falling into the pitfalls confronting them in the nooks and crannies of daily life." 
Resistance to learning is nothing new, but unlike today when not doing one's math homework only results a lack of one skill, resistance to learning meant not acquiring skills that enabled one to survive, and by extension, allowing society to survive. Education was for the most part "functional" rather than knowledge for knowledge's sake . "Simple sins" today like gossip or slander could have far greater ripple effects.
In this light, the severe corporal punishment of the Bible was perfectly appropriate for its time, and in that light, critics are without grounds on the presumed actions of "unreasonable" people.