The contradictions in the book of Leviticus are minimal. This is largely because unlike the books of Genesis, Exodus, and Numbers, the book of Leviticus was composed by one priestly guild, the Aaronids. So it displays a natural unity, cohesion, and theological thrust. Indeed, we’ll encounter contradictions and inconsistencies within the Priestly source itself, but most of them will be between the Priestly writer and the Deuteronomist. The contradictions that the Priestly writer had vis-à-vis how the earlier Yahwist and Elohist narrated Israel’s ancient traditions have already been treated in our study of the books of Genesis and Exodus.
Leviticus 1-7 originally existed as a separate document, one which provided instructions (torah) on preparing Yahweh’s sacrificial offerings. In fact you can read Exodus 40 then go directly to Leviticus 8. You don’t miss a beat in the narrative and Leviticus 8 makes for a better continuation from Exodus 40.
The Priestly writers spent more time addressing the specifics of the cult, sacrifices, distinguishing the pure from the impure, festival observances, the priesthood, etc. (see The Priestly Writer).
“All fat is Yahweh’s! It is an eternal law through your generations, in all your homes. You shall not eat any fat and any blood.” (Lev 3:17)
In the Priestly sacrificial cult, blood was deemed the life-force and any consumption of it was strictly forbidden. Blood also has an expiatory or purifying role in the sacrifices. It was dashed against the altar (#137-138), and the individual’s sin or uncleanliness was expunged.
The fat of the sacrificial animal was deemed Yahweh’s portion. Remember, Leviticus 3 discusses the well-being or peace offering. It is the sacrifice used when one/a family wanted to consume meat. The animal is brought forward to Yahweh’s altar and slaughtered by the individual. The Aaronid priest then dashes its blood on the holy altar and cuts away the animal’s fat and kidneys, and burns “it to smoke on the altar: food, an offering by fire to Yahweh.”
Since the context of this chapter is Yahweh’s sacrificial animals (cow, sheep, goat), we would assume that the prohibition against eating its fat only extended to these animals. Thus Leviticus 7:23-24, which prohibits the eating of the fat of other animals.
We also notice that this prohibition is presented in both Leviticus 3:16-17 and 7:23-27 together with the prohibition not to eat blood. But when we turn to the Deuteronomic tradition, the prohibition against eating fat is not mentioned at all. This is not an explicit contradiction, but by remaining silent on the issue, the Deuteronomic text suggests that eating fat was permissible.
In fact, it looks as if the Priestly text of Leviticus 7:23-27 is responding directly to the Deuteronomist’s failure to address the issue of eating fat. D’s silence makes it permissible. P’s text, however, takes as its given that people are in fact eating the fat of game/nonsacrificial animals. The Priestly writer therefore specifies that this too is prohibited!