The standard reason why a woman giving birth offers a sin offering is that she needs to atone for her vowing never to have a child. The כלי יקר says that this sacrifice is connected to the sin of Eve in the Garden of Eden.
The lesson to be learned was the need for discipline. Judaism is very much based on discipline and waiting. We wait three years before we can eat the fruit of a newly planted tree. We wait to pray before eating and we don’t eat until we make a Bracha.
Husband and wife wait for Mikva until they are reunited each month. The ability to wait not only teaches discipline but it is the very thing that brings about holiness. Judaism allows us to partake of physical pleasures of this world. It is the time and place when we partake that brings about Kedusha. Waiting and discipline are the ingredients that bring about holiness.