My thesis is that the New Covenant is a distinctly different covenant with a distinctly different substance and a distinctly different administration, not to mention, a distinctly different purpose, from that of the Old Covenant. Hence, this discontinuity leaves us with no other option than a credobaptist understanding where Christian baptism is concerned.
The New Covenant is called new in Jer. 31:31; Luke 22:20; 2 Cor. 3:6; Hebrews 8:13; 9:15; 12:24. It is called a better covenant in Heb. 7:22; 8:6. It is called an everlasting covenant in Jer. 32:40; 31:33, 34; 50:5; Isa. 55:3; Ezek. 37:26.
For the law was given through Moses; grace and truth were realized through Jesus Christ. (Jn. 1:17) This statement captures the essential difference between the Old and the New Covenant. One was a covenant of law, the other a covenant of grace and truth. The discontinuity is hard to miss.
Now, if the New Covenant is referred to as new in the Old Testament, and in the New Testament, and it is referred to as a better covenant in the New Testament, and finally, it is referred to as an everlasting covenant, then it seems to me that strong exegetical backing is necessary to warrant any view that would take the two covenants as really just one covenant with two different administrations. With all due respect to our Presbyterian brothers, I do not find such support in their arguments.