|ו וּבִמְלֹאת יְמֵי טָהֳרָהּ, לְבֵן אוֹ לְבַת, תָּבִיא כֶּבֶשׂ בֶּן-שְׁנָתוֹ לְעֹלָה, וּבֶן-יוֹנָה אוֹ-תֹר לְחַטָּאת--אֶל-פֶּתַח אֹהֶל-מוֹעֵד, אֶל-הַכֹּהֵן.||6 And when the days of her purification are fulfilled, for a son, or for a daughter, she shall bring a lamb of the first year for a burnt-offering, and a young pigeon, or a turtle-dove, for a sin-offering, unto the door of the tent of meeting, unto the priest.|
השאלה הד׳ למה חייבה תורה ליולדת להביא
חטאת ועולה כי הנה ענין העולה לא
היה לה צורך במקום הזה והחטאת גם כן
לא היתה ראויה כיון שלא ימצאו לה עון אשר
חטא . ולמה בכל המקומות זכר שיקריבו החטאת
קודם העולה כמו שהתבאר במה שקדם וכאן
זכר ראשונה החטאת :
The fourth question is why does the Torah obligate the woman who gives birth to bring a sin offering and a burnt offering? There is no need for her to bring a burnt offering in this place and also the sin offering is not proper for her since we do not find that she sinned. Also, why is the sin offering mentioned before the burnt offering (Olah) whenever the Torah mentions the bringing of these sacrifices (korbanos), but here the Torah mentions the Burnt offering (Olah) first?
The Abarbanel really hits the nail on the head here. Why on earth should the woman that gives birth have to bring any Korbanos (sacrifices)? It is especially peculiar because she is said to have to bring a burnt offering and a sin offering. Why on earth would she have to bring these two types of sacrifices? What sin did she commit? Also, the reason for bringing an Olah is brought down at the end of the Midrash Tanchuma in Parshat (Parshas) Tzav (13):
The Abarbanel offers his answers for this question, but I would like to offer my own thoughts. The woman needs to first bring the Olah, even though in every other circumstance the sin offering is brought first. What is unique about this Olah?
The classic answer for what sin this woman committed is that she swore that she would never be with her husband again. Essentially, she was screaming in pain, "You did this to me, YOU (exploitive deleted), I hate you!"
With this in mind I think it is fairly simple to understand why a woman in this situation would have to bring both an Olah and a sin offering. Normally, a person brings the sin offering first because that is the more severe situation. The Gemara in Zevachim goes into the reasons why a sin offering is brought first, but I think it is readily understandable. You bring a sin offering first because actions speak louder than words or thoughts. A normal sin is something that effects a persons relationship with G-D or another person. In order to fix that, a person must first show signs of regret, manifested by the sin offering. Essentially, the sin offering shows, "What I did to you was wrong and I apalogize." Then you can bring an Olah which says I am sorry that I even thought about doing this terrible deed. However, the reason the Olah is brought second is because the action is much worse than the thought.
However, by a husband and wife, the relationship is what creates the bond between them. In essence, the action against the other person in this situation is less severe than the thought. The husband and wife might do things which upset each other, but the connection between them is strong enough that they will still love each other and continue to live together. However, when the woman yells, "I am never going near you again!" She is cutting that relationship status that is so strong. In this situation, it is the Olah that must come first because the thought of destroying that relationship is much more severe. The unspoken bond and the tight intangible connection that husband and wife have is broken once the thoughts of severance pop into her head. Therefore, the sin offering takes the back seat to the Olah in this situation. The Olah is brought to show that the wife really wants the relationship. Once that is settled then the sin offering can be brought and the husband and wife's relationship can be restored.
This allows us to understand why the woman must bring an Olah offering, a sin offering and why they must be brought in this order. The most important part about these korbanos is the reestablishment of the husband and wife's relationship. With this idea, the requirements on the woman can be understood in a meaningful way.
(As a side note, Rashi brings down the Gemara which says the Torah might have written the Olah before the sin offering, but really the sin offering comes first in practice. This answer makes very little sense to me. There is no explanation as to why the Torah would write it this way. If anyone knows the answer please let me know.)