Because Christ is the second person of the Trinity, and the perfection of the Law. What Christ was proclaiming, was a sort of verbal abrogation (and perfection) of OT Law.
There are also privileges Moses begged for, being divorce for the Jews due to the hardness of their hearts. With Christ's (direct) proclamations, the place for a Moses as a head-priest is directly subsumed by Christ, and Moses's interpretative authority is thus placed upon St. Peter and the Apostles.