(א) וַיְדַבֵּ֥ר יי אֶל־מֹשֶׁ֥ה לֵּאמֹֽר׃ (ב) דַּבֵּ֞ר אֶל־בְּנֵ֤י יִשְׂרָאֵל֙ לֵאמֹ֔ר אִשָּׁה֙ כִּ֣י תַזְרִ֔יעַ וְיָלְדָ֖ה זָכָ֑ר וְטָֽמְאָה֙ שִׁבְעַ֣ת יָמִ֔ים כִּימֵ֛י נִדַּ֥ת דְּוֺתָ֖הּ תִּטְמָֽא׃ ... (ה) וְאִם־נְקֵבָ֣ה תֵלֵ֔ד וְטָמְאָ֥ה שְׁבֻעַ֖יִם כְּנִדָּתָ֑הּ וְשִׁשִּׁ֥ים יוֹם֙ וְשֵׁ֣שֶׁת יָמִ֔ים תֵּשֵׁ֖ב עַל־דְּמֵ֥י טָהֳרָֽה׃
(1) Hashem spoke to Moses, saying: (2) Speak to the Jewish people thus: When a woman conceives and gives birth to male, she shall be tameh for seven days as during her menstruation ... (5) If she gives birth to a female, she shall be tameh for two weeks as during her menstruation...
(ו) וּבִמְלֹ֣את ׀ יְמֵ֣י טָהֳרָ֗הּ לְבֵן֮ א֣וֹ לְבַת֒ תָּבִ֞יא כֶּ֤בֶשׂ בֶּן־שְׁנָתוֹ֙ לְעֹלָ֔ה וּבֶן־יוֹנָ֥ה אוֹ־תֹ֖ר לְחַטָּ֑את אֶל־פֶּ֥תַח אֹֽהֶל־מוֹעֵ֖ד אֶל־הַכֹּהֵֽן׃ ...
(ח) וְאִם־לֹ֨א תִמְצָ֣א יָדָהּ֮ דֵּ֣י שֶׂה֒ וְלָקְחָ֣ה שְׁתֵּֽי־תֹרִ֗ים א֤וֹ שְׁנֵי֙ בְּנֵ֣י יוֹנָ֔ה אֶחָ֥ד לְעֹלָ֖ה וְאֶחָ֣ד לְחַטָּ֑את וְכִפֶּ֥ר עָלֶ֛יהָ הַכֹּהֵ֖ן וְטָהֵֽרָה׃ (פ)
6. And when the days of her purification have been completed, whether for a son or for a daughter, she shall bring a sheep in its first year as a burnt offering, and a young dove or a turtle dove as a sin offering, to the entrance of the Tent of Meeting, to the kohen…
8. And if she cannot afford a sheep, she shall take two turtledoves or two young doves: one as a burnt offering and one as a sin offering. And the kohen shall effect atonement for her, and she shall become clean.
Rashi
One as a burnt-offering and one as a sin-offering: Scripture places [the burnt-offering] before [the sin-offering] only insofar as how they must be read [in the Torah. ... But the sacrificing of the sin-offering precedes [that of] the burnt-offering. Thus we learned in Zevachim (90a.)
Niddah 31b
Rabbi Simeon ben Yochai was asked by his disciples: Why did the Torah ordain that a woman after childbirth should bring a sacrifice? He replied: When she kneels in bearing she swears impetuously that she will have no intercourse with her husband. The Torah, therefore, ordained that she should bring a sacrifice.
Soforno, Tazria 12:8
Since during her entire impure menstruation days her thoughts were preoccupied with the reproductive organs, therefore she is not fit to enter the Temple until she brings the sacrifice and purifies herself, and then she directs herself to the Temple.
Abarbanel, Tazria
Since a person does not suffer in this world unless he has committed a sin… And a woman who give's birth suffers tremendously during labor, therefore she must bring an offering.
Rabbeinu B'Chayei, Tazria
A Proper explanation would be that she is not bringing an offering for a sin of her own, rather because of her mother (Eve) who was the mother of all humanity… And therefore the Torah obligates her to bring an offering; to atone for the “original sin”
To the woman He said, "I shall surely increase your sorrow and your pregnancy; in pain you shall bear children."
Orach Chayim, Chukas
A man owned two vessels one was full of honey the other full of garbage. He took these vessels outside. All the flies and insects converged on the honey filled vessel, while the garbage filled vessel, although it attracted some insects, it does not compare to the honey vessel.
So too when a Jew passes away, since he is full of sweet and serene holiness, when the soul leaves and the body remains empty the impurities gather in infinite numbers. These are the impure powers which always desire to attach themselves to holiness to enjoy its sweetness.
Sifra, Tazria (Zevachim 90a)
Whenever the Chatas offering is brought to atone for a sin, it is mentioned prior to the Olah offering. Here where it’s not brought due to a sin the Olah offering is mentioned first.
“And [otherwise] when my Lord the king shall sleep with his fathers, and I and my son Solomon shall be lacking."
Shir Hashirim Rabbah 1:15
"Your eyes are like doves"– Just as a dove from when it finds a mate it never exchanges its mate for another. So to with the Jews from when they committed to the Almighty they never exchanged Him for another.