The laws governing the sacrificial system reveal the deep foundations of the relationship between God and His creations. Unlike a human king who relies on gifts from his subjects, God has no need for offerings. The commandments and sacrificial laws were given entirely to guide and benefit humanity [אלשיך].
This dynamic is evident in the types of offerings God prefers. Sacrifices brought out of free will and gratitude, such as the thanksgiving offering, are favored over mandatory offerings brought to atone for a sin. Furthermore, the thanksgiving offering is mostly eaten by the person bringing it rather than being completely burned on the altar. This shows that the purpose of the offering is not to supply the altar with meat, but to elevate the person spiritually [אלשיך].
These laws also reflect God's mercy toward all creatures. The requirement to wait until the eighth day of an animal's life before it can be offered allows the newborn to spend its first seven days with its mother. At the same time, offering a life to God represents a higher spiritual level and an even greater form of mercy than a regular physical existence, which is why the animal becomes acceptable for an offering from the eighth day onward.
The waiting period is not designed merely to honor the altar, nor is it meant to increase the number of sacrifices. This is seen in the strict rule against slaughtering an animal and its offspring on the same day, a limit that actively reduces how many sacrifices can be brought [אלשיך]. Ultimately, God's essence remains entirely complete and unchanging. The entire framework of these commandments exists purely out of His desire to do good for people and provide them with spiritual merit [אלשיך].