

Here is the situation surrounding this statement by Jesus:
The ecclesiastical Jewish teachers were thus testing Jesus' interpretation and application of instructions given by Moses at least 1,000 years before.

Is Jesus contradicting Moses? 

Certainly not. As evidenced in the Old Testament, Moses acted on the instructions of the Supreme Being as he presented rules that the people of that time and circumstance were to live by. They were appropriate, in other words, for that culture and society at that particular time and circumstance. As Moses was God's servant, these rules were ultimately determined by the Supreme Being. God utilized Moses as His representative, evidenced clearly by this statement:
The Israelites did just what the LORD commanded Moses and Aaron. (Exodus 12:28)
This is no different than Jesus' situation with respect to representing God. Consider this statement by Jesus:
"I am not here on my own, but He who sent me is true. You do not know Him, but I know Him because I am from Him and He sent me." (John 7:28-29)
This is clear that Jesus’ teachings were not coming from himself. “He sent me” makes the relationship very clear. The Supreme Being sent Jesus, and Jesus was representing the Supreme Being. Jesus’ teachings were coming from the Supreme Being. God was the source of Jesus’ teachings, and Jesus was His messenger.

So why are some of God's instructions different between Moses and Jesus?

Some of God's instructions changed because the society changed.

In Jesus' time, the rule of law was much more established than in Moses' time. In the society of Jesus' time, there was a strong government that tried criminals and governed by a rule of law. During Moses' time, the Israelites were organizing themselves from living and traveling in the desert. They had previously been slaves in Egypt.

Basic rules grounded in fairness yet applicable to the survivalist situation were applicable. These rules were to prevent them from becoming wild animals that hurt each other and have sex with each other's husbands and wives. In that circumstance, God led Moses to establish rules and enforcement to create order. During Jesus' time, the Roman government combined with the Jewish system provided the rule of law that provided the enforcement. While stonings were still conducted - when decided upon by a council - Jesus recognized this government and rule of law. Consider Jesus' statement:
"Give to Caesar what is Caesar's, and to God what is God's." (Matt. 22:21)
So the time and circumstances had drastically changed, and the culture and society Jesus taught to had different needs than the culture Moses instructed. A government was already in place and enforcement was provided.

We can also relate the difference between Jesus' time and today's culture. For example, beatings, crucifixions and stonings were common in Jesus' time for punishing criminals. In today’s society, we wouldn’t hear of such ghastly practices.

In the same way that society has changed since Jesus’ day, society had changed from Moses’ day to Jesus’ day. From Moses' to Jesus' times, the culture had also become more secular. Today, even more so.

The Supreme Being will adjust His specific instructions to the time and circumstance. The rules He establishes are not His key objectives. God is not setting up rules just to set up rules. He sets up rules and gives instructions through His loving servants to establish an environment that will encourage us to decide to return to Him.

Yes, the Supreme Being wants us back. 

Why? Because He loves us. He knows that we will only be happy when we are back with Him, sharing the relationship of love that we originally shared before we ate the forbidden fruit of envy. As symbolized in Genesis, once we ate the forbidden fruit of envy and wanted to enjoy as God enjoys, the Supreme Being sent us away to the physical world:
What are garments of skin? Are we talking animal skins? No, this is human skin. We are talking about the physical body - covered with skin. Because Adam disobeyed God and ate the fruit of self-centeredness, God banished him from the Garden of Eden - the spiritual world - and we took on temporary physical bodies (garments of skin).
So the LORD God banished him from the Garden of Eden to work the ground from which he [his physical body] had been taken. (Genesis 3:23)
Why were we banished? We were banished because we became envious of the Supreme Being. We wanted to enjoy like the Supreme Being. Consider this statement, made by God about Adam after he ate the fruit:
Remember, this is the Supreme Being speaking. What is "like one of Us," and what does "knowing good and evil" mean? Why would we want to become like God?

God created three types of individuals. One type is His direct expansions. These companions are imbued with all His power and authority ("Us"). The second are partial expansions - which have individuality yet are inseparable from Him as His constant companions. The third type is His separated expansions - each of us. We are also His companions but in the mood of loving servants.

We were given the freedom to love Him or not. 

This freedom is symbolized by the tree of knowledge. Those who did not eat of the tree - those who decided to obey the Supreme Being - love Him so much they don't care about self-enjoyment. They are satisfied with pleasing God and seeing God enjoy: They are happy in their natural position God's loving servants.

'Knowing good and evil' means we wanted more. As clarified here, the correct translation of "good and evil" - טוב (towb) and רע (ra`) - is pleasure and pain - specifically self-centered pleasure and pain.

In other words, each of us fell from the spiritual realm because we were seeking to enjoy separately from the Supreme Being. The expression of this desire is self-centered pleasure, and the consequence of self-centered pleasure is pain.

We cannot have one without the other. 

Thus the Supreme Being created the physical world - a world with duality - of pleasure and pain - so we could exercise our desire to try to enjoy separately from Him.

We must remember that Adam was given the choice of whether to eat the symbolic fruit or not. Why would God have put the tree and the fruit there otherwise? The fact that he put it there "in the center of the garden" represents that choice lies at the center of love for the Supreme Being. He perpetually gives us the choice to love Him or not, because how can there be love without choice?

So what is this physical world then? The physical world is the place where those who choose not to love the Supreme Being go. Here we can ignore God, and even deny God's existence if we want. This is how much freedom the Supreme Being gives us with respect to our relationship with Him.

But this physical world is also place of learning. Here the Supreme Being has set up numerous lessons for us to learn, according to our desires and level of consciousness. Most of these lessons relate to consequences: "as you sow, so shall you reap."

Yes, we each get back what we put out. This is a universal law because this law was programmed into the physical world in order to create fairness - and to teach us.

Or did we expect that the Supreme Being would toss us out of the spiritual realm with no chance of return? Certainly not. The Supreme Being wants us back.

So He sends His loving servants to us to try to canvas us to decide to come back to Him. During that process, He may also impart certain instructions through His representatives, in order to help us grow spiritually and remember Him. Some of the rules are specific to the time and circumstance, however. They are provided by God's representative to those who are present at that particular time. While some of those instructions might also be applicable to later generations, some are not. For some, we must derive their substance.

The lesson in Jesus' instruction above about stoning is forgiveness and humility. He is instructing those around him to look at our issues before we sit in judgment of others.

In fact, we have no real ability to sit in judgment of anyone else. Only the Supreme Being has this ability - because only He understands all of the circumstances.

And the Supreme Being is a fair Judge. But He isn't only a good judge: He is also lovable in so many other ways. He is caring, compassionate, fun, humorous, exciting, wonderful and intelligent. This is why Jesus asks us to love the Supreme Being. Because He is lovable: