Why was the sin offering burned outside the camp?

Ordinarily, the priests eat the sin offering — that's the rule stated plainly in Leviticus 6:26 and 6:29. But one class of sin offering is never eaten at all:

"No sin offering shall be eaten from which any blood is brought into the tent of meeting to make atonement in the Holy Place; it shall be burned with fire." — Leviticus 6:30

The logic turns on where the blood goes. When a sin offering atones for an ordinary Israelite, the priest eats the meat as part of carrying the offerer's guilt. But when the blood is carried into the Tent's interior — which happens when the offering atones for the priest himself, for the whole priesthood, or for the entire nation (Leviticus 4) — the men who would normally eat it are the very people the offering atones for. A priest cannot consume what has been offered for his own sin. So instead the carcass is carried outside the camp and burned. This same pattern goes back to the priests' own ordination, where the sin-offering bull was burned "with fire outside the camp" (Exodus 29:14) — the rite that installed Aaron already showed that the offering which cleanses the priesthood cannot be eaten by the priesthood.

The rule reaches its highest stakes on the Day of Atonement, when the bull and goat whose blood is brought into the Most Holy Place have their bodies carried "outside the camp" and burned (Leviticus 16:27) — the closest textual parallel to Leviticus 6:30 in the whole unit.

This is the very cluster the letter to the Hebrews reads onto the cross:

"The bodies of those animals whose blood is brought into the holy places by the high priest as a sacrifice for sin are burned outside the camp. So Jesus also suffered outside the gate in order to sanctify the people through his own blood." — Hebrews 13:11-12

Two Greek verbs are exact reuses of the Septuagint's wording for this rule — "brought in" (εἰσφέρω, G1533) and "burned up" (κατακαίω, G2618) are the very words used at Leviticus 6:23 and 16:27, not paraphrases. But one word is deliberately changed: where Leviticus says "outside the camp" (G3925), Hebrews says "outside the gate" (G4439) — trading the wilderness camp for Jerusalem's city wall. Because the other two verbs are exact, this one change reads as an intentional substitution rather than a loose citation: the same principle relocated to the author's own world. Jesus, like the sin offering whose blood was brought inside, suffered his death outside the place of holiness.

The full study on The Priests' Portion traces this rule from its wilderness origin at Aaron's ordination, through the test case in Leviticus 10 where Moses himself invokes it, to its fulfillment at the cross.