A newborn animal must remain with its mother. For the first week of its life, neither the mother nor its offspring can be brought as an offering (Leviticus 22:27). It is possible that the Torah is recognizing an animal’s basic “attachment” needs and therefore it would be cruel to separate mother and child at birth.
Consistent connection to a loving caretaker is crucial for healthy development. If this applies to a sheep, how much more so, to a human being. In the first 15 months of human life, having the presence of a loving, reliable, responsive adult gives the child the feeling of security that it’s OK to exist. A sense of safe, secure existence is the foundation for the exploring, identifying and achieving that follow.