Response to Matthew 5

I think that "fulfill" here means two things.  

First, Jesus is the fulfillment of the law.  That means that the entire law/levitical structure was pointing towards Him.  After His death and resurrection, that structure was fulfilled, or completed.  We're now under the new covenant, bound by grace and not adherence to the levitical statutes. 

Second, He fulfilled the law by explaining the law.  His teaching expounded the conventional understanding of the law.  Meaning, as God, He clearly taught what was meant by the law when it was given (by Himself).  

The most important example of this is His usage of Hosea 6:6:

Matthew 12:7   New International Version (NIV)

7 If you had known what these words mean, ‘I desire mercy, not sacrifice,’[a](A) you would not have condemned the innocent.

Matthew 9:13New International Version (NIV)

13 But go and learn what this means: ‘I desire mercy, not sacrifice.’[a](A) For I have not come to call the righteous, but sinners.”(B)

His aim here is the spirit of the law.  In both contexts He is addressing Pharisees who have called Him on the carpet for superficial "violations" of the law.  They've missed the point.  

Mercy trumps the moral high ground.  Mercy trumps being "right."  Mercy is better than sacrifice or piety or religious stature.  The point of the law is MERCY.  Mercy most clearly demonstrates who God is.  And the Pharisees completely missed it.  

Does this mean the law is gone?  Nope.

Romans 5:19-21New International Version (NIV)

19 For just as through the disobedience of the one man(A) the many were made sinners,(B) so also through the obedience(C) of the one man the many will be made righteous.

20 The law was brought in so that the trespass might increase.(D) But where sin increased, grace increased all the more,(E) 21 so that, just as sin reigned in death,(F) so also grace(G) might reign through righteousness to bring eternal life(H) through Jesus Christ our Lord.

So Jesus said your righteousness must exceed that of the Pharisees to enter the kingdom of heaven.  No one can ever do that!  Except Jesus.  

Here comes imputed righteousness. 

So the law maintains God's justice.  If there was no price for sin, God would not be just.  He would be a lazy Father raising bratty children with no consequences for their actions.  

However, God is merciful and just!  So because of His mercy, at great cost to Himself, He satisfied his own perfect standard with a perfect sacrifice.  Because of Jesus’ sinless life, death, and resurrection, we are under the law of His grace!!  Jesus’ righteousness is counted as our own, meeting God’s standard for perfection while our obvious imperfection is perpetually covered by the grace of Jesus. 

So God is just.  God is mercy.  The law is fulfilled.  The law is satisfied.  We receive grace as we are being made more like Christ until the day we are perfected (completed) in Him.