Why does Christ's blood atone?

from comment127 here http://www.calledtocommunion.com/2010/04/catholic-and-reformed-conceptions-of-the-atonement/

"... why does Christ’s blood atone. The blood represents the very life. To give one’s possessions (e.g. house, property, clothes, money) is to give something external to oneself. But to pour out one’s blood unto death, is to give one’s very self. Hence Jesus says, “Greater love has no man than this, that he lay down his life for his friends.” (Jn. 15:13) This is why His blood is so precious, and St. Peter explains that we “were not redeemed with perishable things like silver or gold from your futile way of life inherited from your forefathers, but with precious blood, as of a lamb unblemished and spotless, the blood of Christ.” (1 Pet. 1:18-19) Christ redeemed us by giving the greatest gift of love, namely, His very life, letting it be poured out for our salvation. By His blood, He offered Himself without blemish to God (Heb 9:14), and by means of this sacrifice made peace with God for us (Col 1:20) and purchased the Church (Acts 20:28; Rev. 5:9). Christ’s blood sanctifies us (and the NT frequently alludes to the OT practice of cleansing things by the sprinkling of blood) because through this perfect offering to God, Christ won for us the sanctifying grace and agape by which we are sanctified."