Likely in response to false teachers in Corinth who were teaching the Old Covenant (i.e., that people are saved by faith in Jesus PLUS obeying the Law), Paul had 3 things to say: (1) the New Covenant has greater glory than the Old Covenant [7-11], (2) the Jews have a veil over their hearts [12-18], and (3) Paul compared and contrasted the Old and New Covenants, by using names, nicknames, verbs and adjectives woven like a thread throughout these verses.  In doing so, Paul made it clear that the New Covenant is far superior to the Old Covenant.  

2 Corinthians 3:7-18