In The Book Of Romans, Paul wrote,

Romans 5:12 Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned.

When man sinned in the Garden, death entered. It is logical, then, that for man to overcome death, He must remove sin from his life. The problem is that death did a thorough work on man through his sin. The result of our first parent's sin was man's spirit being separated from God's fellowship, never being able to come to union with Him because of his sin. How, then could man find restoration? God has spoken clearly in His word and has told us that the way to reconciliation with Him is through the shedding of blood. But not just any blood sacrifice will do. That which would be sacrificed must be perfect to atone for the perfect, yet innocent, life Adam slew in the Garden: his own, and that of all of his offspring who would come forth from him. This was man's dilemma: Adam's race could only bring forth imperfect life, sinful life that was separated from God and would never serve as a sacrifice for sin. God, therefore, had to provide man with the sacrifice he could not produce, and He did that by sending Jesus to become our sin offering.

God's way of atonement is given in Leviticus 17:

Leviticus 17:11 For the life of the flesh is in the blood: and I have given it to you upon the altar to make an atonement for your souls: for it is the blood that maketh an atonement for the soul.

The writer to the Hebrews makes this plain, telling us that without the shedding of blood there is no remission of sin:

Hebrews 9:18 Whereupon neither the first testament was dedicated without blood.
19 For when Moses had spoken every precept to all the people according to the law, he took the blood of calves and of goats, with water, and scarlet wool, and hyssop, and sprinkled both the book, and all the people,
20 Saying, This is the blood of the testament which God hath enjoined unto you.
21 Moreover he sprinkled with blood both the tabernacle, and all the vessels of the ministry.
22 And almost all things are by the law purged with blood; and without shedding of blood is no remission.

The shedding of the blood of animals, though, did not contain the fulness of what God wanted to tell humanity concerning the shedding of Blood for the atonement and cleansing of sin, as the writer to the Hebrews explains:

Hebrews 10:4 For it is not possible that the blood of bulls and of goats should take away sins.

Just as the Old Covenant was initiated by the shedding of the blood of animals, so the New Covenant was initiated by the shedding of the blood of Jesus, the Son of God:

Hebrews 10:5 Wherefore when he cometh into the world, he saith, Sacrifice and offering thou wouldest not, but a body hast thou prepared me:
6 In burnt offerings and sacrifices for sin thou hast had no pleasure.
7 Then said I, Lo, I come (in the volume of the book it is written of me,) to do thy will, O God.
8 Above when he said, Sacrifice and offering and burnt offerings and offering for sin thou wouldest not, neither hadst pleasure therein; which are offered by the law;
9 Then said he, Lo, I come to do thy will, O God. He taketh away the first, that he may establish the second.

God wanted humanity to know He had the perfect sacrifice for them and forshadowed that sacrifice by the animals slain in the Old Testament. The blood of animals in the Old Testament had to be shed continually to deal with the sins of the people, but Jesus was sacrificed ONLY ONCE for all men:

Hebrews 7:26 For such an high priest became us, who is holy, harmless, undefiled, separate from sinners, and made higher than the heavens;
27 Who needeth not daily, as those high priests, to offer up sacrifice, first for his own sins, and then for the people's: for this HE DID ONCE, when he offered up himself.
28 For the law maketh men high priests which have infirmity; but the word of the oath, which was since the law, maketh the Son, who is consecrated for evermore.

Hebrews 9:28 So Christ WAS ONCE OFFERED to bear the sins of many; and unto them that look for him shall he appear the second time without sin unto salvation.

Hebrews 10:10 By the which will we are sanctified through the offering of the body of Jesus Christ ONCE FOR ALL.
11 And every priest standeth daily ministering and offering oftentimes the same sacrifices, which can never take away sins:
12 But this man, after he had offered one sacrifice for sins for ever, sat down on the right hand of God;
13 From henceforth expecting till his enemies be made his footstool.
14 For by one offering he hath perfected for ever them that are sanctified.

God has established the one sacrifice for the atonement and cleansing of sin, and that can be received by all men through faith in what Jesus Christ, God's Son, did on Calvary.