Since "sin" in Hebrew means a missing of the mark (you tried to do right and you "missed") what does G-d say about more serious wrongdoings? If they aren't sin, what are they?
What happens if a person commits manslaughter (or theft, or beating someone up) -- acts that were impulsive actions people know are wrong but they "just can't help themselves." These are not "sin" -- there is another term for them in the bible. These are called Avon / עוון (impulsive, lustful acts -- a person couldn't control their urges).
But if Jesus "died for your sins" (totally unbiblical) then he died for your mistakes and not your "big" transgressions. The Christian bible doesn't say that Jesus died for your Avon / עוון or even worse actions!
What about things worse than sin or Avon / עוון? What about things like pre-planned murder, or other evils that are wilfful wrongdoing in defiance of G-d (you know it is wrong, you know G-d forbids it and you defy Him). These are called pĕsha' / פֶּֽשַׁע in the T'nach.
Again, Jesus (per the Christian bible) did not die for your avon / עוון or your pĕsha' / פֶּֽשַׁע --- but just for your mistakes???
In reality human sacrifices are forbidden. No one can die for your sins, your avon / עוון or your pĕsha' / פֶּֽשַׁע. More serious wrongdoings could not be atoned for with blood sacrifices at all
עוון Avon (translated by Christians as iniquity) is an impulsive act of lust or uncontrollable urges (could not be atoned for with a sacrifice). An avon (unless it falls under the asham talu or asham g'zelot) cannot be rectified with a qorban (sacrifice), and neither can a pĕsha' / פֶּֽשַׁע. Repentance and turning to G-d to seek forgiveness for sins against G-d and seeking forgiveness to any person that might have been harmed from that person are the methods of atonement; The generic Hebrew word for any kind of wrongdoing is aveira / עבירה. This is a feminine noun (nouns are either feminine or masculine in Hebrew)..
Cheit / חטא (translated by Christians as sin) translates to a mistake -- a person tried to do the right thing and "missed." For individuals a In Shoftim / Judges 20:16 a group of men are described as "All these could sling a stone at a hair-breadth and not miss." A cheit / חטא could be atoned for with a sacrifice. It was only one of two types of wrong doings which could be atoned for with sacrifice.
Avon / עוון (translated by Christians as iniquity) is an impulsive act of lust or uncontrollable urges. An avon/ עוון (unless it falls under the אָשָׁם תָּלוּי / asham talui or or אָשָׁם גְּזֵל֣וֹת / asham g'zelot) cannot be rectified with a qorban (sacrifice). So what are these two sacrifices which can be brought for an avon/ עוון? They are discussed in Vayikra / Leviticus chapter 5.
Those were the only two types of Avon / עוון (translated by Christians as iniquity) which a person could bring a sacrifice for (an asham / guilt sacrifice). Any other type of Avon / עוון must be atoned for with other actions including charity, prayer, repentance (see the list below). If the sacrifice for either a sin sacrifice or guilt sacrifice was brought it had to meet the following criteria:
1. Is an animal which is physically without blemish; a ram for the Asham (Vayikra / Lev. 5:14); a female goat for the Chatat (sin offering) (Vayikra / Lev. 4:28); male animals or birds for the Olah. (Vayikra / Lev. 1:3, 10, 14). (Olah, translated as "burnt sacrifice" was a voluntary sacrifice generally brought to thank G-d, but sometimes brought for impure thoughts, not deeds).
2. They are all slaughtered in the holy area of the temple and their blood is poured around the outside altar (Vayikra / Lev. 1:4, 4:30; 7:2);
3. Parts of the Asham and Chatat (sin offering) are burnt on top of the altar. All of the Olah (elevation / burnt offering) is burnt there. (Vayikra / Lev. 1:7-8; 4:31; 7:3-5) 4. The Asham and Chatat (sin offering) must be eaten by the priests as opposed to the Olah. (Vayikra / Lev. 6:19; 7:6-7) which is consumed by the fire.
Jews eat kosher animals only – and humans are not kosher. The asham sacrifice can NOT BE A PERSON.
Now, what about the wrongdoings which are worse than making a mistake (the "sin") or a lusftul action you didn't control (guilt)?
Pĕsha' / פֶּֽשַׁע is usually translated by Christians as "transgression." It means to willfully go against G-d. It means "rebellion" (could not be atoned for with a sacrifice) -- but other things in this life do atone for them. 1 Kings 8:46-50 include chatat, avon, rasha (wicked or evil) and pesha are atoned for by prayer. Repentance and turning to G-d to seek forgiveness for sins against G-d and seeking forgiveness to any person that might have been harmed from that person are the methods of atonement;
Ezekiel 18:21-32 speaks of sin, iniquity and willful rebellion against G-d all being forgiven through repentance. chatat (18:21), pesha (18:22), cheit (18:24), pesha (18:28), pesha and avon (18:30) are all atoned through repentance.
"By loving kindness and truth iniquity is atoned for..." (Mishlei / Proverbs 16:6).
"If you return to G-d you will be restored; if you remove unrighteousness far from your tent...then you will delight in G-d..." (Job 22:23-27).
This whole fixation on blood, blood, blood by missionaries is not supported by the Jewish bible. The missionaries take the statement that blood can atone for SOME sins and somehow morph it into "you need blood for sins to be forgiven." This is akin to eating a slice of pizza because you are hungry and then insisting that the only type of food that exists in the world is pizza.
Here is a list showing different things that atone for different types of wrongdoing that disprove the statement in Hebrews 9:22 that
without the shedding of blood there is no forgiveness.
2 Shmuel 12:13-14 / 2 Samuel 12:13-14 is a cheit (David admits to sin before Nathan the prophet and repents)
Yonah / Jonah 3:10 has to do with the sins of Nineveh (unspecified, just identified as "evil" in 1:2), the people repented and G-d forgave
Vayikra / Leviticus 26:40-42 speaks of avon and repentence atoning for it
Yechezkel / Ezekiel 18:21-32 speaks of chatat (21), pesha (22), chatat (24), pesha (28), pesha and avon (30) are all atoned through repentance
Mishlei / Proverbs 16:6 an avon is atoned for with kindness
Daniel 4:24 is chatat and avon by showing mercy and kindness
PRAYER (accompanied by repentance)
Hoshea / Hosea 14:2-3 teshuva (turning to G-d) and 1prayer atones for avon
1 Melachim 8:46-50 / 1 Kings 8:46-50 include chatat, avon, rasha (wicked or evil) and pesha are atoned for by prayer
Daniel 9:5-19 include chatat, avon, and rasha are atoned by prayer
Yeshayahu / Isaiah 27:9 both chatat and avon are atoned by removing idolatry
Yeshayahu / Isaiah 40:1-2 avon is removed by punishment
Eichah / Lamentations 4:22 avon is removed by punishment
Yeshayahu / Isaiah 22:14 avon will surely not be atoned until you die.
Leviticus 5:1-13 for specific ashams (guilts including not testifying honestly, touching something ritually unclean, if one makes an oath one doesn't keep, he must confess, and he must bring a guilt offering which should be a female sheep or goat, but if he can't afford it he may bring two turtle doves (one as a chatat and one as an olah). If he cannot afford the turtle doves he may bring flour as a chatat (sin offer)
Sh'mot / Exodus 30:15-16 to atone for the life-force (similar to blood in Leviticus 17:11)
Bamidbar / Numbers 31:50 to atone for the life-force (similar to blood in Leviticus 17:11)
Bamidbar / Numbers 17:11-12 atonement for the Israelites "for there is wrath" Per Rashi This secret was given over to him by the angel of death when he went up to heaven, that incense holds back the plague… as is related in Tractate Shabbath (89a).
Hopefully this post shows that "sin" is not defined in the bible as Christians have come to define it. It also shows that blood is not necessary for the remission of sin, and that serious wrongdoings could never be atoned for with blood sacrifices, but that prayer, repentence and other methods have always atoned for wrongdoings -- both accidental and intentional.