There are far fewer of these passages, so let’s look at each one in a little more detail, and in their context.
"You have heard that it was said to those of old, 'You shall not murder; and whoever murders will be liable to judgment.' Matthew 5:21
The context of this verse in Matthew 5 is the ‘Sermon on the Mount’. Immediately before this verse, Yeshua says, “I have not come to abolish the Law, but to fulfil it.”
The word translated ‘fulfil’ means to ‘fill up’ as in fill up full of meaning, or, as the Rabbis of the day would have understood it (since they used the phrase themselves) to properly interpret it. To ‘fulfil Torah’ meant to interpret it correctly, full of its intended meaning. To ‘abolish Torah’ meant to disrespect it (to nullify it – Matthew 15:6 and Mark 7:13) and to obscure its intended meaning.
YHVH’s Law is pretty simple. But to live it out is harder, as no law can cover every situation. The Law was given to point out what sin is. It was not meant to provide its own righteousness (though the definition of righteous is one who obeys the Law, and we are called to be righteous) but to point toward the need for a Saviour. The judges were to help decide how to apply the Law…how to ‘fulfil’ it. The Rabbis took on that job. And they recorded all of their decisions (which were often contradictory) and added these laws to the Law, effectively making a burden that nobody could carry. Sound familiar? Look up Matthew 23:4, Luke 11:46, Acts 15:10 and 28, Galatians 5:1, and then Matthew 11:28 as comparison.
If you look up the source of Matthew 5:21 ‘You shall not murder’ you will find it pretty quickly in the 10 Commandments. But where is ‘whoever murders will be liable to judgment’? It is not there, it was added by the Rabbis. Now that doesn’t make it wrong, it makes sense. However, the point of this Law ‘do not murder’ was not to say, ‘if you murder you will be punished’. Yeshua gives the point in the next few verses:
“But I say to you that everyone who is angry with his brother will be liable to judgment; whoever insults his brother will be liable to the council; and whoever says, 'You fool!' will be liable to the hell of fire.”
What the hands do (in this case, murder) isn’t sourced in the hands, it is sourced in the heart (mind). One who doesn’t murder with his hands can still have a heart that commits murder daily. He may not be liable to the judgment of man, but he sure will to the judgment of YHVH!
"You have heard that it was said, 'You shall not commit adultery.' Matthew 5:27
This verse is ALSO what is written, isn’t it? There were many man-made rules on adultery. The rabbinical rulings modified this Law often in favour of the man and harsher to the woman. You can find evidence of this in the first verses of John 8. (This account seems to have been a later addition, it is not in earlier manuscripts and so may or may not be true…however, it clearly shows rabbinic ruling of the day in its conspicuous absence of the man involved in the incidence of adultery.) Again, Yeshua goes on to state the ‘full’ meaning of the commandment. Its not about not getting caught, it is about not even considering the thoughts in the first place, that might lead to the act in the second.
"Again you have heard that it was said to those of old, 'You shall not swear falsely, but shall perform to the Lord what you have sworn.' Matthew 5:33
"You have heard that it was said, 'An eye for an eye and a tooth for a tooth.' Matthew 5:38
"You have heard that it was said, 'You shall love your neighbor and hate your enemy.' Matthew 5:43
There are more examples...but you should be getting the picture...'It is written' refers to direct quotes from the Torah. 'You have heard it said' refers to rabbinic rulings, usually ON a Torah law. These rabbinic rulings were the interpretations of Torah laws, which formed a set of law in themselves.
These human laws became the standard for Judaism on how Torah was to be interpreted. And often they missed the point YHVH had for the law entirely. Yeshua interpreted these laws as they were meant to be understood. They were never meant to govern outward behaviour only, they were meant to point out the state of the heart, to clearly identify sin, and to point towards the coming Saviour.