Contrasting the New Covenant with the Old, the Apostle points out that “the letter,” with its requirements and penalties, “killeth.” Therefore the dispensation of the Law is called “the ministration of condemnation” and “the ministration of death” (II Cor. 3:7,9).
The ministration of the Law began in a blaze of glory. Mount Sinai was “altogether on a smoke… as the smoke of a furnace.” There were thunderings and lightnings and an earthquake. There was the sound of a trumpet, “exceeding loud.” There was the glorious Shekinah cloud in which God Himself appeared and “spake all these words” (Ex. 19:9- 20:1).
But before Moses had even come down from the mount with the tables of stone, the people were breaking the very first commandment, dancing like heathen about a golden calf. From here on the administration of the Law took on another aspect. Judgment had to be pronounced and penalties inflicted. Nor could any escape its just sentence of condemnation and death. What had begun in glory led but to gloom, “because the law worketh wrath…” (Rom. 4:15). “…for it is written: cursed is every one that continueth not in all things which are written in the book of the law to do them” (Gal. 3:10).
But there can be no gloom associated with the ministration of the New Covenant, says the Apostle, for under it righteousness and life are administered to all who will receive them by faith. And this because the claims of the Old Covenant were fully met by Christ at Calvary. Thus the ministration of the New Covenant outshines the ministration of the Old in every respect.
But was not the New Covenant made “with the house of Israel and with the house of Judah,” rather than with the Church of our day? Yes, but with Israel’s rejection of Christ and her temporary blindness the blessings of the New Covenant are now bestowed by grace upon those who do receive Christ. Hence, it was not Peter or the twelve, but Paul who, with his associates, was made an “able minister of the New Testament” (II Cor. 3:6). source