In the Fifth Week of Lent, the Church stressed the eternal priesthood of Christ, the High Priest Who never dies. Today, in this reading from the Letter to the Hebrews, we see the flip-side: Christ is also the eternal sacrifice. The new covenant in Christ replaces the old. While the sacrifices of the old covenant had to be offered over and over and could not bring those who offered them to sanctity, Christ's sacrifice is offered once for all, and in it, we can all reach perfection.
Hebrews 10:1-18
For the law having a shadow of the good things to come, not the very image of the things; by the selfsame sacrifices which they offer continually every year, can never make the comers thereunto perfect: For then they would have ceased to be offered: because the worshippers once cleansed should have no conscience of sin any longer: But in them there is made a commemoration of sins every year. For it is impossible that with the blood of oxen and goats sin should be taken away. Wherefore when he cometh into the world, he saith: Sacrifice and oblation thou wouldest not: but a body thou hast fitted to me: Holocausts for sin did not please thee. Then said I: Behold I come: in the head of the book it is written of me: that I should do thy will, O God.
In saying before, Sacrifices, and oblations, and holocausts for sin thou wouldest not, neither are they pleasing to thee, which are offered according to the law. Then said I: Behold, I come to do thy will, O God: he taketh away the first, that he may establish that which followeth.
In the which will, we are sanctified by the oblation of the body of Jesus Christ once. And every priest indeed standeth daily ministering, and often offering the same sacrifices, which can never take away sins. But this man offering one sacrifice for sins, for ever sitteth on the right hand of God, from henceforth expecting, until his enemies be made his footstool. For by one oblation he hath perfected for ever them that are sanctified.
And the Holy Ghost also doth testify this to us. For after that he said: And this is the testament which I will make unto them after those days, saith the Lord. I will give my laws in their hearts, and on their minds will I write them: And their sins and iniquities I will remember no more. Now where there is a remission of these, there is no more an oblation for sin.
- Source: Douay-Rheims 1899 American Edition of the Bible (in the public domain)

