The Levitical Law lays out the different sacrifices offered for the forgiveness of sins. There are five offerings: Burnt, Grain, Fellowship, Sin, and Guilt. Burnt, Sin, and Guilt offerings are all for the forgiveness of sin. These offerings culminate in the Day of Atonement in which two goats are taken: one as a sin offering, the other as a burnt offering. One is sacrificed as a sin offering, the other, chosen as a burnt offering, becomes a scapegoat.
These two goats live out the experience of sin. Consider Adam and Eve. They experience sin in desiring to hide and be covered and by exile from the garden. Consider Cain and Abel. Cain hides his sin by burying his brother and is exiled. He even complains that he will be hidden from God's presence (Gen. 4:14). Sin brings shame and alienation. The first goat's blood, rather than hiding sin, covers it by cleansing it. It does not cover it up and ignore it; the goat's life-force, its blood, cleanses that aspect of sin, its shame, by uncovering its impact and cleansing it. The second goat, picked as a burnt offering, suffers the exile of sin. The sin of the community is dumped on its head and carries the sin into exile. Notice how the substitution of the goats works: It is not the blood of the people which cleanses their defilement (although some sins do call for death--'their blood is on their own head'), though the sacrifice of the goat reveals the effects of sin; neither is it the people who are exiled because of their sin: sin is exiled on another. The people are spared by the sacrifice of the goats. They are forgiven.
But, of course, forgiveness is not just something received, but something given. For those who were part of the Day of Atonement, not only was their own sin atoned for, but also the sin committed against them. The first goat's blood cleanses the defilement they suffered from another and cleanses the defilement of the other who sinned against them. The exile of the second goat carries the sin of the other away from the community so that they may live in peace with one another. Just as my sin is atoned for, so is the sin against me atoned for. The sacrificial substitute makes my forgiveness possible, and empowers me to forgive.
This is not "just a matter of being in community," as though being in community were a minor issue; being in community is extremely serious, dangerous, and difficult. (Rousseau and Hobbes were right about that; they were wrong in its solution, though.) In fact, community is so serious, dangerous, and difficult that being in imperfect communities means that one suffers the effect of sin. Thanks be to God, however, that the sacrifice of Jesus Christ takes seriously the dangers of community and suffers both the impacts of sin--his blood provided to cleanse consciences and his life living out the exile of Israel in his crucifixion. By this sacrifice, a new community is formed in which sin is fully revealed and dealt with. We are forgiven because Christ bears the results of sin; we forgive because Christ bears the results of sin.