3 Wherefore many things are uttered by Him, far below His proper dignity, and here when He is about to proceed upon His addition to the law, He has used abundance for correction beforehand. For neither was it once only that He said, “I do not abrogate the law,” but He both repeated it again, and added another and a greater thing; in that, to the words, “Think not that I have come to destroy,” He subjoined, “I am not come to destroy, but to fulfill.”
Now this not only obstructs the obstinacy of the Jews, but stops also the mouths of those heretics, who say that the old covenant is of the devil. For if Christ came to destroy his tyranny, how is this covenant not only not destroyed, but even fulfilled by Him? For He said not only, “I do not destroy it;” though this had been enough; but “I even fulfill it:” which are the words of one so far from opposing himself, as to be even establishing it.
And how, one may ask, did He not destroy it? In what way did He rather fulfill either the law or the prophets? The prophets He fulfilled, inasmuch as He confirmed by His actions all that had been said concerning Him; wherefore also the evangelist used to say in each case, “That it might be fulfilled which was spoken by the prophet.” Both when He was born, and when the children sung that wondrous hymn to Him, and when He sat on the ass, and in very many more instances He worked this same fulfillment: all which things must have been unfulfilled, if He had not come.
But the law He fulfilled, not in one way only, but in a second and third also. In one way, by transgressing none of the precepts of the law. For that He did fulfill it all, hear what He says to John, “For thus it becomes us to fulfill all righteousness.” And to the Jews also He said, “Which of you convinces me of sin.” And to His disciples again, “The prince of this world comes, and finds nothing in me.” And the prophet too from the first had said that “He did no sin.”
This then was one sense in which He fulfilled it. Another, that He did the same through us also; for this is the marvel, that He not only Himself fulfilled it, but He granted this to us likewise. Which thing Paul also declaring said, “Christ is the end of the law for righteousness to every one that believes.” And he said also, that “He judged sin in the flesh, that the righteousness of the law might be fulfilled in us who walk not after the flesh.” And again, “Do we then make void the law through faith? God forbid! Yea, we establish the law.” For since the law was laboring at this, to make man righteous, but had not power, He came and brought in the way of righteousness by faith, and so established that which the law desired: and what the law could not by letters, this He accomplished by faith. On this account He says, “I am not come to destroy the law.”
Source: Homilies on the Gospel of St. Matthew (New Advent)