The mystical meaning of this law is as follows:
“Mother” signifies the intellect, since the intellect “gives birth” to the emotions. When the intellect recognizes the virtue of something or someone, it “gives birth” to the emotion of love for it; when it recognizes the undesirability or harmfulness of something or someone, it “gives birth” to the emotion of hatred or fear for it; and so on.
The “animal” signifies the emotions, since animals are driven by their instinctive emotions rather than by intellect.
When an emotion is first “born,” it must be matured by the intellect. This process takes place over the course of seven “days,” i.e., it is a sevenfold process – one for each of the seven basic emotions. Only after the emotions have been matured are they fit to be “an offering for G‑d,” i.e., worthy of becoming part of the psyche of a human being dedicated to G‑d’s service.1

I have never understood why we sacrifice animals. After all, they are innocents by nature, so why do we say it is okay to sacrifice them? Why would a benevolent God, who has told us "Thou Shall Not Kill", then accept this practice of "killing". Surely there must be a better way to serve God!