For the Hebrews there was a specific sacrifice that covered every failure in life. Going to the temple must have been much like going to the barber shop. "Hey George nice to see you. Yeah, I little more off the top this time. Thanks." In you go and out you go... problem solved... you feel better after your haircut (sacrifice) on several levels but the hair just keeps on growing.
The sacrifices involved people you knew because you saw them again and again.
Now instead of doing sacrifices to look right and feel right we go to the one who was the sacrifice and He says, "You look good already. I'll just give those feet of yours a rinsing." We go to Him and confess our sin and He reaffirms that we look fine to Him once and for all and are refreshed. It still involves a personal touch. But there is a reverence and lack of familiarity when we see that the one washing our feet has nail pierced hands. Wounds that should have been on our hands but are not because of God's kindness.