Looking beyond the inefficacy of the Old Covenant Sacrifices, let us look closer at what Jesus told His listeners to do after leaving the gift at the altar:
"Leave there thy gift before the altar, and go thy way; first be reconciled to thy brother, and then come and offer thy gift." (Matthew 5: 24)
"Reconcile" renders the Greek word " διαλλάσσομαι, diallassómai" which means change, exchange, as in "change enmity for friendship." Yet the prefix "diá," indicates "thoroughly," which intensifies the meaning to render a "complete change."
The same term is used in Pauls second Epistle to the Corinthians:
"18And all things are of God, who hath reconciled us to himself by Jesus Christ, and hath given to us the ministry of reconciliation;
To wit, that God was in Christ, reconciling the world unto himself, not imputing their trespasses unto them; and hath committed unto us the word of reconciliation." (2 Corinthians 5: 18-19)
Here, the word "reconcile" renders the Greek word "katallassó: to change, exchange, reconcile
καταλλάσσω goes further than διαλλάσσω, for where "δια" speaks of "thoroughly", "κατα" indicates a far greater reconciliation, one which is "down to an exact point,"
Where Jesus demands a "thorough reconciliation" in the Sermon on the Mount, by His death He provides for us a complete, thorough, permanent, permeated, and impermeable reconciliation, with His Father and the world!
We are expected to perform a "thorough reconcilation" with every person who has ought with us, an impossible order — yet through His death and resurrection, Christ Jesus has accomplished this for us. Instead of drawing up an inexhaustive list of aggrieved parties, we can trust in the blood of our Savior to make our standing right with all who may have ought with us — and there is no other way than through Him!