The quote that Jesus brings to this statement is from Hosea 6:6, when God spoke through Hosea and said:
"For I desire mercy, not sacrifice, and acknowledgment of God rather than burnt offerings."
Jesus compares this situation to when David and his companions ate consecrated bread from the temple, and the fact that this went against Jewish law.
Jesus also points out here that the scriptures say that when temple priests ate bread on the Sabbath, they were not guilty of breaking the law.
Jesus is comparing himself and his disciples to David and his companions - and the temple priests who also broke the law of the Sabbath. What do they have in common?
What they have in common is that they were all loving servants of God, involved in using their lives to please the Supreme Being.
This is why Jesus says here:
"I tell you that One greater than the temple is here."
Many ecclesiastical teachers have interpreted this statement to mean that Jesus is calling himself "One greater than the temple." But would Jesus really make this kind of statement about himself? Is this the same Jesus who said:
"For I have come down from heaven not to do my will but to do the will of Him who sent me." (John 6:38)
"For whoever does the will of my Father in heaven is my brother and sister and mother.” (Matt. 12:50)
“My teaching is not my own. It comes from the One who sent me." (John 7:16)
Notice the use of "the One" in the last quote - and its use ("One greater") here: They are the same. Jesus is obviously not considering himself "One greater than the temple." This is an attribute that can only be made to "the One" who sent Jesus - the Father - the Supreme Being.
And this is the common bond between the comparison between himself, David and the priests with regard to following Jewish law. Jesus is saying that he is serving the Supreme Being. And the Supreme Being is thus present in those works.
As such, that service on behalf of the Supreme Being would qualify as trumping the ritualistic Jewish laws.
Why? Because the Supreme Being is the Owner and Controller of everything. Therefore, He is not subject to any laws - all laws come from Him - therefore He is not subject to them.
This is the meaning of Jesus' statement: "I tell you that One greater than the temple is here."
And what about "the son of man is lord of the Sabbath"? What does this mean?
Since he was speaking of the activities of David, and the priests, he could not be saying he is the only 'lord of the sabbath'.
It would also be odd for Jesus to be speaking about himself in third person, right after discussing David and the priests. Isn't he comparing his activity with theirs? Why would he then eliminate them from being "sons of man"? And if he did, why would he say it in the third person?
How many people do this when they speak? If a person named Tom were to feel hungry, would he say “Tom is hungry”? No. He would say “I am hungry.” Likewise, if Jesus were to be speaking specifically of himself here he would have used "I", "me" or "my." This would be common sense, and very clear. Also note that Matthew does not indicate that Jesus himself was eating out of the field - Jesus was defending his disciples' activity.
This relates directly to the meaning of the phrase "son of man." For many, this is mysterious title, which Jesus often talked about frequently, with respect to doing God's will. Typically he used this to describe what seems to be himself, but always in the third person. What does "son of man" mean anyway?
The word "son" in these texts was translated from the Greek word υἱός (huios - one who depends on another or is his follower). The most appropriate translation here is not physical offspring, but one of servitude. This more precise meaning lies with the notion that during those times a son was typically the devoted servant of his father. This means Jesus is referring to himself, his disciples, David, and priests in sacrifice all as devoted servants of mankind or humanity. In other words, Jesus is identifying that these humble and devoted disciples eating out on the Sabbath are doing God's service by supporting his preaching, and thus serving humanity.
Consider this as David humbly commits to God about himself:
O Lord, what is man that you care for him, the son of man [servant of humanity] that you think of him? (Psalm 144:3)
And God repeatedly called Ezekiel the "son of man" [servant of humanity] as He spoke to him in the Book of Ezekiel.
As such, the correct translation of this last sentence above would then rightfully be:
“For the servant of humanity rules the Sabbath.”
This would also capture the essence and meaning of Jesus’ statements prior to this last sentence. Jesus is explaining, for example, with the Hosea quote, that what the Supreme Being wants from us is our loving service, not necessarily following rituals: ‘I desire mercy, not sacrifice,’
The use of "mercy" here in Hosea and by Jesus refers to service that pleases God and helps others realize their relationship with the Supreme Being. This means being compassionate upon others. If a person has heard the Truth about the Supreme Being, and he is merciful to others, that person will pass the Truth on to them. This is mercy, and this is captured by the title, "servant of humanity."
The Supreme Being wants us to acknowledge Him with love and devotion in practical ways. Just following a bunch of rituals for the sake of being accepted by our peers or by a religious group or church doesn’t please the Supreme Being. The Supreme Being wants us to develop our own personal relationship with Him, and do practical things to please Him - which relates directly to praising Him, glorifying Him and honoring Him - Our Best Friend and Eternal Protector - before others. This is "mercy."
(For a translation of Jesus' statements from the Book of Matthew without institutional sectarian influence, see the Gospels of Jesus - translated from the original Greek texts.)