We shall look at this passage in two parts:
The first part is where Paul is sensing-perhaps as he reads through what he has just had written- that his claim that the Corinthians are a living letter of Jesus produced under his ministry may sound a little like self-praise. He hastens to insist that whatever is done is not his own work, but the work of God. The Holy Spirit has moved within listeners' hearts and made him adequate for the task of preaching and debating. Rather than this attitude causing Paul to have severe hindrances in his work, it enabled him to do far more than he would humanly do because he knew that God was by his side, giving him the strength, protection, guidance and gifts for each task.
The second part of this passage contrasts the old and new covenants, the word defined as an arrangement between two people through which they enter into a certain relationship-the covenant of marriage, for example. There is an essential variation between that sort of covenant and the Biblical covenant, in that Biblical covenants, by their nature, do not involve two equal partners because Almighty God is the prime mover and it is He who approaches humans to offer them a relationship upon conditions which they cannot initiate or alter, only accept or reject.
The new covenant which God offered mankind through the sacrifice of Jesus Christ is radically different from the old, offered through the Law. The old was based on a written document-Exodus 24 v 1-8-whereas the new is based on the power of the life-giving Spirit. The old was external; the new changes a person's heart: '' I will give you a new heart and put a new spirit in you; I will remove from you your heart of stone and give you a heart of flesh.'' Ezekiel 36 v 26. The issue with the old covenant was that it was possible to obey it externally whilst rejecting it in one's heart. The new is superior in that the Spirit comes into the heart and changes it! The old covenant produced a legal relationship between God and man, essentially making God the Judge and human beings always in debt because the bar was set impossibly high. It caused hopelessness, frustration, a permanent sense of condemnation and helplessness.
The new covenant is one based on love. Men and women were no longer essentially criminals, they were children of God. It told them what to do, but gave them the strength to do it too!
The orthodox Jews rejected the new and stayed with the old, but the old was never intended to be the ultimate, it was a step along the way.. As someone wrote: 'When the sun has risen, the lamps cease to be of use'.