Why is the veil still on the heart of the average Jewish person today?
The veil remains because of blindness and unbelief: the average Jewish person continues reading Moses and the Torah in synagogue, still tying himself to the Law, and cannot see that Christ's death, burial, and resurrection ended the Law and brought salvation by grace through faith.
Les explains that their minds were blinded, and until this day the same veil remains untaken away when the Old Testament is read. The veil is not taken away because the Law is done away in Christ: when Christ finished redemption by His death, burial, and resurrection, the whole system of Law was abolished, and something far better came. The Law was given to Israel to prepare them for Messiah, but in unbelief they failed it; God still carried out His plan and revealed to Paul salvation by faith because of grace, nothing added. So the average Jew in blindness still ties himself to the Law, with the veil still on Moses' head, unable to see that it has come to an end. In synagogue they sincerely read the Torah, from Moses, but the veil keeps them from seeing that it has passed off the scene; it remains upon their heart. Les notes Paul wrote around A.D. 60, but the same truth applied in 1997.
But their minds were blinded: for until this day remaineth the same vail untaken away in the reading of the old testament; which vail is done away in Christ.
But even unto this day, when Moses is read, the vail is upon their heart.