Can I put my son to death, as is taught in the Law?
You’re presumably referring to Deuteronomy 21:18-21:
“If a man has a stubborn and rebellious son, who will not obey the voice of his father or the voice of his mother, and, though they chastise him, will not give heed to them, then his father and his mother shall take hold of him and bring him out to the elders of his city at the gate of the place where he lives, and they shall say to the elders of his city, ‘This our son is stubborn and rebellious, he will not obey our voice; he is a glutton and a drunkard.’ Then all the men of the city shall stone him to death with stones; so you shall purge the evil from your midst; and all Israel shall hear, and fear” (21:18-21).
To be clear, a father could not inflict death on his son unilaterally. As the passage conveys, the father had to refer his case to his city’s elders. But why does God the Father allow the killing of a son in this case, while his divine Son Jesus Christ spoke against killing a woman caught in serious moral misbehavior, specifically adultery (John 8), which was also a capital crime in the Mosaic Law, as the Jewish leaders noted to Jesus?
Because the wages of sin is death (Rom. 6:23), such killing as noted in Deuteronomy 21 is not intrinsically evil, and because God’s people at that time in salvation history had demonstrated themselves to be less morally developed, God was more permissive in allowing capital punishment, lest worse moral evils befall his people—namely, those which can lead to eternal death, not simply temporal death.
In addition, such an executed son would not be beyond God’s mercy regarding his eternal salvation, as only the merciful Lord can judge perfectly the subjective state of one’s soul at his death, and one may repent as he’s undergoing capital punishment as he realizes his particular judgment before God is imminent.
Jesus fulfills/perfects the law (Matt. 5:17-18; 43-48), and he shows mankind’s true moral destiny in him, explained in his Sermon on the Mount (Matt. 5 - Matt. 7) and fulfilled through his incomparable and atoning self-sacrifice of Calvary (see John 15:13). Jesus shows mercy to the woman caught in adultery, yet he doesn’t preclude capital punishment in all cases, as St. Paul further affirms (see Acts 25:10-11, Rom. 13:1-4).
Consequently, you may not kill your son. But if he commits a crime, you should turn him into the police, though make sure you get a priest to visit him so that he can repent, confess his sins and receive God’s absolution in the sacrament of reconciliation (see John 20:21-23).