The conscience is a funny thing.
"For if the blood of bulls and of goats, and the ashes of an heifer sprinkling the unclean, sanctifieth to the purifying of the flesh:
How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God?" - Hebrews 9:13-14 KJV
Unlike material objects the conscience isn't cleaned by soap or detergent.
Did blood purify? Why? An eye for an eye works on the conscience. You hurt me so I hurt you and balance is preserved. Even children get this. No one needs to teach it. Children need to unlearn it.
Adam's wounds are incurable. He wounds others to balance things out. Terrible... but true.
'I'm sorry.' is a substitute but often a poor one for aching Adam.
God gave an animal sacrifice to Adam. Blood was spilled. It is terrible really it is. An innocent thing dying because of his mistake or just outright transgression... but it is that way. Innocents suffer because of mistakes and that old conscience gets stains no on can seem to reach.
If blood for blood worked, and it did to a degree, then how much more does what Jesus did work?
Like I said the conscience isn't like an object. We can clean something even if it doesn't want to be clean with soap but the conscience must believe that the substitute is good enough.
"For we did not follow cleverly devised myths when we made known to you the power and coming of our Lord Jesus Christ, but we were eyewitnesses of his majesty. For when he received honor and glory from God the Father, and the voice was borne to him by the Majestic Glory, 'This is my beloved Son, with whom I am well pleased,' " - 2 Peter 1:16-17 ESV
God the Father thinks His Son is good enough. He raised him from the dead because He found Him more than acceptable.
I think we lapse in this and start to 'do things.' What things? The bible calls them 'dead works' and they are all the things that a person who has a dirty conscience does.
"Looking unto Jesus the author and finisher of our faith; who for the joy that was set before him endured the cross, despising the shame, and is set down at the right hand of the throne of God." - Hebrews 12:2 KJV
Jesus isn't just the beginning of our faith. He Is the finisher also. We can live with a clean conscience and have it cleansed again and again.
"How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God?" - Hebrews 9:14 KJV
An eye for an eye just made everyone hurt. Jesus gives all the parties who believe peace without retaliation. No one else can reach that far into a man or woman.
No one else can clean the soul.