In the Sermon on the Mount (Matthew chapters 5,6,7), Jesus indeed set the bar far higher than that of the Law.
Jesus did this many times by saying “You have heard that it was said…”,(and then refers to the particular law), and then He would go on to say, “But I say to you…”, (and He then goes on to raise the bar even higher).
Here is an example:
Matthew 5:27, 28 AMPC
27 You have heard that it was said, You shall not commit adultery. 28 But I say to you that everyone who so much as looks at a woman with evil desire for her has already committed adultery with her in his heart.
Here is another example;
Matthew 5:43, 44 AMPC
43 You have heard that it was said, You shall love your neighbor and hate your enemy; 44 But I tell you, Love your enemies and pray for those who persecute you,
You pointed out that the Law was strict and yet here in each of these examples that Jesus speaks of, the hearer is confronted with an astoundingly higher and practically impossible standard.
So, why did Jesus do this?
I believe it was because Jesus was illustrating just how high the bar of the holiness of God, actually is … and how impossible it is for a man to attain it by his own effort.
Jesus wanted them to come to the end of themselves.
Matthew 5:20 ESV
For I tell you, unless your righteousness exceeds that of the scribes and Pharisees, you will never enter the kingdom of heaven.
After saying many such things, Jesus then leads His hearers to a stunning crescendo of the Sermon on The Mount in Ch 7 by concluding that those who Hear His Words but do not Do or Practice them, are hypocrites, but those who are wise, are those who are both Hearers and Doers.
Which would have left his hearers astonished and thinking “how can we even hope to keep such high laws? such that even the thoughts of our hearts are completely pure?, how can our righteousness ever hope to exceed that of the Scribes and Pharisees? How can we ever enter the Kingdom of Heaven then?”.
Of course, you and I when we hear this, must also ask ourselves “how can we keep these laws?”
The answer is: We cannot.
Matthew 5:17 ESV
Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them.
Romans 3:20-25 ESV
20 For by works of the law no human being will be justified in his sight, since through the law comes knowledge of sin. 21 But now the righteousness of God has been manifested apart from the law, although the Law and the Prophets bear witness to it— 22 the righteousness of God through faith in Jesus Christ for all who believe. For there is no distinction: 23 for all have sinned and fall short of the glory of God, 24 and are justified by his grace as a gift, through the redemption that is in Christ Jesus, 25 whom God put forward as a propitiation by his blood, to be received by faith
It is only Jesus, alone, who has kept the perfect and Holy and high law of God.
We, fail. Miserably.
Our ability to emulate all that Jesus taught us in the Sermon on the Mount, lies in our being Born Again in Him, receiving His righteousness, and being given new hearts, onto which He writes the Law of love, by which we then seek to Love God with all our heart, mind, soul and strength, and to love our neighbour as our selves, through the empowerment of His Holy Spirit, and in doing so, we keep the Law of God, not by the measure of rules, but by the measure of love in our hearts.
Because all the Law and the Prophets are summed up in this,
Matthew 22:37-40 NKJV
37 Jesus said to him, “‘You shall love the Lord your God with all your heart, with all your soul, and with all your mind.’ 38 This is the first and great commandment. 39 And the second is like it: ‘You shall love your neighbor as yourself.’ 40 On these two commandments hang all the Law and the Prophets.”
This is why Love is the fulfillment of the Law and prophets.
And this is why Sin = Lack of Love.
Sin, misses the mark.. of Love.