God considers blood special whether it is from animals or people. "For the life of a creature is in the blood . . ." (Leviticus 17:11). Blood is needed for atonement. It is Jesus' blood, however, that makes it possible to receive everasting atonement.
I have heard it said that Christians don't live under a sacrificial system. The truth is, we don't utilize animal sacrifices anymore but we still live under a sacrificial system. It is the once-and-for-all sacrifice of Jesus (Hebrews 9:23-28). Remember, "It is the blood that makes atonement for one's life" (Leviticus 17:11).