“ . . . not like Moses, who would put a veil over his face so that the Israelites might not gaze at the outcome of what was being brought to an end.” [2 Cor. 3:13 ESV]
Moses veiled his face when he came down the mountain for two reasons (Ex 34:29 ff). The first reason is that the people were afraid to come near him. Paul elaborates that Moses veiled his face because the glory faded revealing he was not a spiritual superhero, but human--and humanity comes to an end.
“But their minds were hardened. For to this day, when they read the old covenant, that same veil remains unlifted, because only through Christ is it taken away. Yes, to this day whenever Moses is read a veil lies over their hearts.” [2 Cor 3:14-15 ESV]
The second reason Moses veiled his face was because the people were blinded (lit. “made hard”--like stone) in their own spirituality.
Even while on his deathbed the Parson wears the veil. The minister uses his dying breath to give us the only clue we have as to why he wore the veil: you are all hypocrites, everyone wears a black veil, shielding their eyes from God as they draw around themselves people who make them comfortable. When the Parson dies he is buried with his face covered.
The Old Covenant was a preview of what was coming and they could not see it. The people were blinded in their own spirituality.