Lets once again leave the interpretations on the side and see the confession of the Master Himself.
"For I did not speak on My own initiative, but the Father Himself who sent Me has given Me a commandment as to what to say and what to speak.
Therefore Jesus answered and was saying to them, "Truly, truly, I say to you, the Son can do nothing of Himself, unless it is something He sees the Father doing; for whatever the Father does, these things the Son also does in like manner.
"Do you not believe that I am in the Father, and the Father is in Me? The words that I say to you I do not speak on My own initiative, but the Father abiding in Me does His works.
More importantly as a prophet of Israel like Moses (Deut. 18:18) could not do, teach or say ANYTHING that was contrary to the Law of God. According to Deuteronomy 13, Christ would not be the Messiah if he did not do and teach the Law of God, or taught contrary to the Law of God.
Its amazing how simple it is to understand Scripture when you use the Law and the Prophets as a litmus test, just like Christ and His followers did.
"But this I admit to you, that according to the Way which they call a sect I do serve the God of our fathers, believing everything that is in accordance with the Law and that is written in the Prophets; [Acts 24:14]
If it agrees with the Law and the Prophets, accept it. If not reject it! After all, even Christ Himself would not be Christ, unless He brought to fruition what was prophesied and spoken of Him in the Law and the Prophets. This is why He always used the Law and the Prophets to prove who He was!
Now He said to them, "These are My words which I spoke to you while I was still with you, that all things which are written about Me in the Law of Moses and the Prophets and the Psalms must be fulfilled."
Then He opened their minds to understand the Scriptures [Luke 24.]
So yes Jesus taught the Law, Jesus taught from the Law, Jesus kept the Law, Jesus taught that the Law will not pass away, Jesus taught us to do and teach even the least of Gods commandments, Jesus taught us to do good on the Sabbath, Jesus taught us to the deep Spiritual meaning of the Law, Jesus is the goal of the Law!