The atonement process as described in the Torah contained many nuanced elements. Essentially, after a person repented, forgiveness was fully granted — for the core of repentance as required by the Torah is simply the abandonment of sin (Deut. 4:27-35; Deut. 30:1-6; Isaiah 55:6-7; Hosea 14:2-3). In addition, it is important to note that a crucial element found within the Torah definition of "repentance" is to demonstrate a change in the attitudes that made possible... the initial violation of HaShem’s command.
So why was sacrifice sometimes a part of the atonement process? In some cases, certain specific sins were so “damaging” — the added step of offering a sacrifice was required… in addition to receiving forgiveness. The Hebrew word “cheit” often translated as “sin” can have many shades of meaning within the sacrificial system…such as with the “sin” offering. In this context, the term “cheit” is not always understood as “sin” in the Torah. Sometimes “cheit” should be defined as “purify” or “cleanse” — such as when the Altar in the Sanctuary was “purified" — "vaychatei” for use by HaShem (Lev. 8:15; Lev; 14:49; Lev 16; Numbers 19:9).
In light of this meaning we can now answer the question “why sacrifice?” Some sins leave a “blemish” or “stain” on the essential part of a person. Thus, the “damage” referred to above becomes evident in a persons “personality.” In other words, with certain sins a person lessons their own spiritual self worth, leaving a “blemish” on their original “personality” or “core being” — thus impairing one’s own spiritual integrity (Psalm 51).
In truth, while a person is forgiven for their sin through heartfelt repentance (Isaiah 40:1-2; Isaiah 55:6-9; 2 Samuel 13; 1 Kings 8:46-53)— the “personality” can remain “stained” by the sin. So the sacrificial process added to the forgiveness already received, by “purifying” the “personality” thus restoring it to its previous pure status. Therefore, the meaning of the root word for “sacrifice” or “korban” actually means to “draw near” to HaShem (Ecclesiastes 4:17) via the “cheit” or “purification” of our “core being” (Ezekiel 36:22-29). This is why the first steps taken in understanding the “sin” offering — should first be by grasping its fundamental nature... as a “purification" offering.
It is important for every Torah Jew to remember that there were numerous other steps and details involved in the atonement process… beside the death of an animal (Isaiah 1:11-20). So every sincere step taken in the process was considered a step upward. In reality, the atonement process is the Heavenly opportunity to journey into one’s soul, thus turning the service of the Altar… into the service of the heart (Eccl. 4:17-5:6).