Today, I decided to read St. John Chrysostom's Homily 16. He starts by quoting this passage:
"Think not that I have come to destroy the Law or the Prophets." (Matt. 5:17)
And then, being the genius that he is, thoroughly explains what it meant.
It's too subtle to explain it all in one blogpost.
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.
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." (Romans 10:4) 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." (Romans 8:3-4) And again, "Do we then make void the law through faith? God forbid! Yea, we establish the law." (Romans 3:31) 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."
4. But if any one will inquire accurately, he will find also another, a third sense, in which this has been done. Of what sort is it then? In the sense of that future code of laws, which He was about to deliver to them.
For His sayings were no repeal of the former, but a drawing out, and filling up of them. Thus, "not to kill," is not annulled by the saying, Be not angry, but rather is filled up and put in greater security: and so of all the others.
Later on he writes:
He does not, you see, find fault with the old law, but will have it made stricter. Whereas, had it been evil, He would not have required more of it; He would not have made it more perfect, but would have cast it out.
The point being that the third way the Law is fulfilled is that by making it stricter, he safeguards from future sin AND he makes us holier, for disciplining ourselves to a higher standard.
It's very good. I encourage you to take a look if you need some spiritual reading.