The inauguration of the Tabernacle was more than a momentous historical event; it served as a living classroom for the priesthood. The precise actions performed during these days were not just a one-time ceremony, but a practical model that shaped the future of the Tabernacle service. Rather than simply stating that the instructions were carried out as God commanded, the detailed account of burning the fats and organs was necessary to guide the priests in future offerings. Because these events occurred before the general laws of sacrifices were fully taught, this detailed record established the permanent rules for offering, pressing hands on the animal, slaughtering, and dashing the blood for all future generations [מלבי״ם, אדרת אליהו].
Although the process of skinning the animal is noticeably absent from the account, it is naturally implied, as an animal cannot be cut into its respective parts without first removing its hide [אדרת אליהו]. However, this step is intentionally left unmentioned out of respect for Moses. As the leader of the people, it was considered beneath his dignity to engage in the mundane task of handling and taking the animal skins [מלבי״ם].
When detailing the removal of the inner fats, the account is remarkably concise. While instructions elsewhere distinguish between the thick layer of fat covering the innards and the smaller amounts found on the sides, they are combined here into a single brief concept because, ultimately, both rest upon the innards [אבן עזרא]. Furthermore, the primary approach among commentators notes a subtle shift regarding the appendage of the liver. By comparing the events here with parallel instructions given earlier, they conclude that the priest is not meant to remove the appendage alone. Instead, a small piece of the liver itself must be taken together with it [רש״י, מזרחי, שפתי חכמים, גור אריה, דברי דוד].