Why Aren’t Sacrifices Necessary for Atonement Today if Remission of Sin is Only Through Blood?

The author of Hebrews 9 makes the claim:

"And almost all things are by the law purged with blood; and without shedding of blood is no remission."

(Hebrews 9:22)

The author seemingly bases this on the verse in Leviticus:

^“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.”

(Leviticus 17:11)

In Old Testament belief, sacrifice is merely a means of making it easier to come closer to God. But that's not all God wants for remission of sin. Stating that blood facilitates the process in some way is certainly not an indication that without blood there is no remission of sin. This non-sequiter is purely a New Testament teaching.

Some sources that make this clear are:
a) "Take with you words, and turn to the LORD: say unto him, Take away all iniquity, and receive us graciously: so will we render the calves of our lips."

(Hosea 14:2)

b) "The sacrifices of God are a broken spirit: a broken and a contrite heart, O God, thou wilt not despise"

(Psalm 51:17)

c) The city of Nineveh was saved from doom because:

"And God saw their works, that they turned from their evil way; and God repented of the evil, that he had said that he would do unto them; and he did it not."

(Jonah 3:10)

d) God says that He doesn't need sacrifices:

"Will I eat the flesh of bulls, or drink the blood of goats? Offer unto God thanksgiving; and pay thy vows unto the most High: And call upon me in the day of trouble: I will deliver thee, and thou shalt glorify me. ."

e) God makes it clear that it's good deeds, not sacrifice that counts:

""With what shall I come before the LORD, and bow myself before God on high? Shall I come before him with burnt offerings, with calves a year old? Will the LORD be pleased with thousands of rams, with ten thousands of rivers of oil? Shall I give my first-born for my transgression, the fruit of my body for the sin of my soul?" He has showed you, O man, what is good; and what does the LORD require of you but to do justice, and to love kindness, and to walk humbly with your God? ."

(Micah 6:6-8)

So it is clear that whereas the Christian system believes that blood effects atonement, in the Hebrew system it's repentance, contrition and prayer.

As far as Jesus being the "Lamb of God", this again is solely a NT concept.

According to the Hebrew Scriptures, the only animals permitted for sacrificial purposes are those that have split hooves and chew their cud. The carcass of an unclean animal defiles (Leviticus 11:26). On these grounds alone, human beings are disqualified for sacrificial purposes. Jesus, as a human being, was unfit for sacrificial purposes.

An animal blood atonement offering must be physically unblemished (Leviticus 22:18-25). According to the evangelists, Jesus was physically abused prior to his execution (Matthew 27:26, Mark 15:15, John 19:1; John 20:25; Matthew 27:29, Mark 15:17, John 19:2). According to Paul, Jesus' circumcision constituted "mutilation" (Philippians 3:2) and is likened to "castration" (Galatians 5:12). As a result, Jesus would again be disqualified as a valid sacrifice.

The New Testament's claim that Jesus' death was "one sacrifice for sin for all time" (Hebrews 10:12) is not supported by the Hebrew Scriptures. Mere death, no matter what was the extent of the preceding violence or pain, does not satisfy the biblical requirements for those times when a blood atonement sacrifice is offered. In a blood atonement offering the animal (clean species and unblemished) must actually die as a result of blood loss. That is why it is called "a blood atonement sacrifice."

Jesus (unclean human species and blemished) did not die within the Temple precinct, at the hands of an Aaronic priest, or through the shedding of blood. Jesus' blood was not sprinkled on the altar by the Aaronic high priest (Leviticus 16:18-19). Animal sacrifice, offered as a blood atonement, must conform to the biblical guidelines set down in Leviticus 17:11: (a) Bloodshed (by means of shechitah--Deuteronomy 12:21), (b) Given solely to the Jewish people, (c) Blood sprinkled upon the Temple altar.

Jesus' humanity, the physical state of his body, and the manner of his death (crucifixion) do not satisfy any blood atonement provisions found in the Hebrew Scriptures.

Summary:

Both beliefs agree:

a) God commanded that literal goat and sheep sacrifices are part of atonement for some (not all) sins.
b) Presently, the literal goat and sheep sacrifices are not necessary, and nor are they possible, and they've been replaced with some other means of achieving the same.

They disagree as to WHAT they are replaced with.

Christians believe it's the figurative sacrifice of Jesus. (Human sacrifice is not supported by OT scripture, and is called an “abomination” in Jeremiah 32:35)

Hebrew Scripture teaches that it's repentance, prayer, and contrition.

What Christians making the claim that the Old Testament would demand sacrifices are trying to do is on one hand state that they acknowledge that literal goat and sheep sacrifices are not necessary, as they have been replaced by another figurative means, while holding Old Testament believers to the premise that there is no substitute.

This is using different measures for each of the two groups.