Cordial greetings and a very good day.
Legitimate distinctions must be made, dear friend, between legislation given to Israel as a theocratic state under Moses and the more universal revelation given to mankind through Noah. Noah stood at the head of a new human race after the Flood and stipulations of the Noahic covenant, such as the permission to meat, the promise of no further universal flood and the death penalty mandate, applied not just to Noah and his family or to some limited ethnic group, but, in principle, to all mankind.
It is, dear friend, the reference to man being created in God’s image in Genesis 9: 6 that gives the rationale for the death penalty. When violence in the form of murder is done to a man, it is in effect and outrage against Almighty God and such murderous violence demands retributive justice to redress the disorder caused by the offence. “For this reason the traditional teaching of the Church has acknowledged the right and duty of legitimate public authority to punish malefactors by means of penalties commensurate with the gravity of crime, not excluding, in cases of extreme gravity, the death penalty” (CCC, para. 2266, added emphasis mine). Moreover, since there has been no suspension of man being made in the image of God, the rationale for the death penalty in Genesis 9: 6 is as true today as it was in the days of Noah. It follows that while the detailed provisions of the criminal code of Israel are no longer binding under the New Covenant, the mandate, and it is a mandate, requiring the death penalty for murder remains one of continuing validity.
St. Paul describes (Rom. 13: 4) the civil authority as “the minister of God” because it is charged with a function which has been explicitly forbidden to the private individual (cf. Rom. 12: 17a, 19). The state, dear friend, has been delegated the right and duty to be “a revenger to execute wrath upon him that doeth evil”, which includes the infliction of death penalty for murder in accordance with the original God-given mandate (Gen. 9: 6). In point of fact, the sanctity of life actually validates the death penalty for the heinous crime of murder, besides restoring a disturbed moral balance.
Unfortunately, dear friend, in our post-Christian age the whole concept of retributive justice is no longer fashionable and men have come to see capital punishment as evidence of the dehumanization of a society that officially kills its members. It is also said that plain revenge is the real motive behind demands for wanting the death of perpetrator of murder. Certainly, one must concur that that is not a worthy Christian motive for any action, not just capital punishment, but that is not the reason why the Church in its constant teaching has always held the death penalty to be morally licit and permissible.
Warmest good wishes,