Jesus says other, similar things in this same passage. But, the teaching is clear: Under the Mosaic Law, people were forbidden to commit adultery and murder. However, Jesus (in the New Covenant) requires us to go further than that, for, under the Old Covenant, people would only keep the letter of these Laws and not go any deeper than that - because nothing required that they do so. For example, the Commandment “Thou shall not kill” was limited to the legal wording of the Commandment. According to the Pharisees, as long as one kept the specific legal conditions of the Commandment, one was “righteous before God.” Jesus denies this. For the Lord Jesus, the mere letter of the Law is not enough because, while the Commandment says, “Thou shall not kill,” it does not mean that you are righteous if you just beat a man within an inch of his life, just as long as you do not actually kill him.

That was never God’s intention at all. Rather, the Commandment goes much deeper than that and Christians are obligated (by their Covenant of Love with Jesus Christ) to keep the Commandment much deeper than that. However, non-Christian Jews are not. They are only bound by the specific wording of the Commandment; that is, they are bound by the letter of the law, and on a mere basis of law. Christians are bound by the righteousness of Christ Himself (to Whom the Law points) because of their Covenant of Love with Jesus Christ. See the distinction?
Now, it should be pointed out that Jesus is not saying that looking at a woman lustfully or calling your brother a fool is the very same thing as physically cheating on your wife or physically killing your brother, for the latter sins are far more serious than the former. Rather, the Lord’s point is that we are called to a righteousness and a perfection that is so high that, not only would we never commit adultery or murder, but we would not even harbor lustful or unjustly violent thoughts in our hearts; that is, we are called to avoid even those things, for the sake of our love of Jesus and our desire to be perfect as He is perfect. Again, do you see the distinction?
And this is what Jesus means when, at the beginning of the passage in Matthew 5, He says …
“Do not think that I have come to abolish the Law or the Prophets. I have not come to abolish but to fulfill. …I tell you, unless your righteousness surpasses that of the scribes and pharisees, you will not enter the Kingdom of Heaven.”
In other words, the Law must be kept in a way that is greater than a mere legal observance of the Commandments. It must be exceeded by the example of Him Who embodies the Righteousness behind the Law: Jesus Christ. This is why Christians are not bound by the Law, but by the New Covenant of grace and love in Jesus Christ. Sunday, is the day the fulfillment of the New Covenant in Love – not in Law - (and an anticipation of the day of the coming of the Lord of Love in glory) when the Divine Food that binds us to this Covenant is received by those united in the fullness of His Church.
Adventists, with their strong fixation on the OT, have adopted a very legal-minded attitude toward obeying God that is far more Jewish than it is Christian. But, again, we in the New Covenant are not a people of “law,” but a people of grace who live in a Covenant based on Love. No “law” binds you or any Christian to Jesus Christ; rather, you are bound to Him by a Covenant of Faith and Love, and you obey Him because of that Covenant of Faith and Love (per Hebrews 5:9, Romans 16:26, etc). Obedience does not have to be based on Law. Obedience can be based on faith and love, and the latter is the nature of the New Covenant in Christ. This is the Good News of the Gospel, and the Adventists are largely blind to it.