The law could never make us right with God because sin weakened it's power making it incapable of saving us. Our sin nature defeated us from the get go, so we never stood a chance of being able to fulfill the law by doing what it says. The entire nature of man without the Holy Spirit was vulnerable and held in captivity to sin under the control of darkness, we were powerless to help ourselves. In that sense, the law was never able to us to bring us salvation and yet it held the key to breaking the bondage of captivity that we were held in.
However, while we were weak and powerless, God sent Jesus to come in the flesh and utterly destroy the power of darkness. It is important to realize that Jesus came into the world and was just as much human as he was God. He was born under the same captivity that you and I were born into and yet he never sinned. He lived a perfect life and so he was able to fulfill the entire law because sin never defeated him. He came as our representative before God to stand in the gap that sin created. Just as Adam plunged the world into sin, Jesus rescued the world from sin.
Now to do this, Jesus became a sin offering for us. This is amazing, because Jesus is holy, he abhors sin, so this was no small sacrifice becoming the very thing that he hated and despised. But according to the law a sin offering was required. There were instructions for many sacrifices according to the Old Testament law. Leviticus 7:37 records six of them. However, a constant throughout all instructions for these different offerings was that a substitution was made for the individual making the offering. Something was sacrificed and the atonement was imputed to the individual making the sacrifice.
The interesting thing about the guidelines for the sin offering was that it had to made whether or not the sin committed was intentional or unintentional. The party for whom the sacrifice was made would lay their hands upon the offering to symbolically transfer guilt to the animal. Then the blood was sprinkled over everything because the covering of blood brought atonement and the forgiveness of sins. The sin offering was offered over and over because it was only a temporary solution to the problem. Hebrews chapter 10 says, "those sacrifices are an annual reminder of sins, because it is impossible for the blood of bulls and goats to take away sins." ( Hebrews 10:3-4 ). So there was a need for the sin offering to be made, but it was apparent that the law was not able to accomplish the reconciliation and removal of guilt, because the sin consciousness was still there afterwards.
Concerning the law and sacrifices, Hebrews say this, "This is an illustration for the present time, indicating that the gifts and sacrifices being offered were not able to clear the conscience of the worshiper. They are only a matter of food and drink and various ceremonial washings-external regulations applying until the time of the new order" ( Hebrews 9:9-10 ). That is because we were so defeated by sin that the blood covering of animals would never do. So, what it could not do, 'God did by sending his own Son in the likeness of sinful man to be a sin offering' ( Romans 8:3 ). This is an amazing truth because Hebrews 8 goes on to tell us that Christ did not enter a manmade tabernacle nor did he enter with bulls and goats, but he enter a heavenly tabernacle with his own blood obtaining eternal redemption for us. This blood so pure and so holy, unblemished before God, was able to save completely and cleanse our consciences from any guilt remaining ( Hebrews 9:12-14 ). And so he completely defeated death and overcame sin in one redemptive act.
Because Jesus only died to sin once, sin has been completely taken care of. He condemned it in the flesh when he died upon the cross. He subdued it, he overcame it, he deprived it of all it's power over us. The law was never able to do that for us, but what the law could not do, Christ did!
For those of us who have accepted this payment, We have traded our sin and our sin nature and have been given the righteousness of God. This righteousness fulfills the law which was always God's intent. It wasn't on our own account, but it was a gift. Through Christ we have become the righteousness of God. "For our sake He made Christ [virtually] to be sin Who knew no sin, so that in and through Him we might become [endued with, viewed as being in, and examples of] the righteousness of God [what we ought to be, approved and acceptable and in right relationship with Him, by His goodness]" ( II Corinthians 5:21 Amp ).
The blood of Christ was able to cleanse us for all guilt. When we understand this, then we should no longer have a sin consciousness. That sin sensitivity will keep us from enjoying all the benefits of an intimate relationship with the Lord. But if we can overcome this notion of guilt then we will have boldness before the God. Hebrews 10 says, "let us draw near to God with a sincere heart in full assurance of faith, having our hearts sprinkled to cleanse us from a guilty conscience and having our bodies washed with pure water" ( Hebrews 10:22 ). Meaning that we should continually be approaching God this way, in boldness. We should have no consciousness of guilt because we are so totally forgiven through Christ. His blood was able to completely wipe away all condemnation that sin held over us.
Today, I am so thankful that Jesus did for us, what the law was incapable of doing. It is my prayer that you start approaching God in full assurance of faith, with boldness before him. Start living like you've been redeemed, fully purchased by precious blood, reveling in grace. God bless you!