Shared ground
These verses show the peace offering as a carefully ordered ritual carried out by the newly installed priesthood. Aaron kills the animals for the people, his sons assist by bringing the blood, and Aaron applies the blood to the altar all around it (explicit). The best internal portions (“fat,” kidneys, and the liver-related covering) are set apart and burned on the altar (explicit), while the breasts and right thigh are not burned but are formally presented before Yahweh by a “wave” action (explicit).
The passage also highlights role-sharing: the sons handle support tasks, while Aaron performs the key altar actions and the public presentation (inference from the sequence). The repeated “as Moses commanded” underscores that acceptable worship here means following the given instructions rather than improvising (explicit).
Where interpretation differs
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What the “wave” action looked like. The text says the breasts and right thigh were “waved” before Yahweh, but does not describe the motion. Some think it involved lifting and moving the portion in a visible presentation; others think it may have been a more limited gesture of raising or extending it before the altar.
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What exactly “the cover of the liver” refers to. Translations and explanations differ on whether this means a particular lobe, a membrane, or an attached fatty piece. The passage’s main point, though, is that a specific liver-associated portion is reserved for the altar.
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Why the fat is placed “on the breasts” before burning. Some read this as a practical staging step (setting the fat on the meat before transferring it to burn). Others think it signals a moment of presentation: the priestly portions (breast/thigh) are marked out, while the fat portion is then burned to Yahweh.
Why the disagreement exists
The Hebrew ritual terms are brief and assume shared knowledge of tabernacle practice. The passage narrates actions without explaining mechanics, and later instructions elsewhere in Leviticus give categories of portions without always spelling out the gesture details. That leaves room for reconstruction from language, comparison with nearby passages, and reasonable guesses about ceremony.
What this passage clearly contributes
It clarifies that the peace offering involves both an altar portion (fat and specified internal parts burned) and presented portions (breast and right thigh waved before Yahweh). It also shows the priesthood functioning as mediator for “the people,” with blood applied around the altar and with certain portions formally designated for Yahweh and for priestly handling, all under the authority of the instructions given through Moses (Leviticus 9:21).