Today's Mass readings work together in a pretty amazing way, even though they were not specifically intended to. In the first reading (2 Cor 3:15-4:1-3, 6), Paul uses an image from the book of Exodus to explain that, as magnificent as the Covenant of Sinai was, it can't compare to the glory that Jesus ushered in. In the Gospel, Jesus refers back to the prescriptions of the Sinai Law, too. In the Sermon on the Mount, he tells his followers that they have to go beyond the basic demands of the Law ("You shall not kill") to an even more godlike way of living ("whoever is angry with his brother...is liable to judgment").
Both Jesus and Paul hint that the "new" was already present in the "old"; all they are doing is "taking away the veil" so we can see clearly what God had in mind all along. We're moving, Paul says, "from one degree of glory to another."