פּירוש אויף ויקרא 12:8

אחד לעלה ואחד לחטאת THE ONE FOR A BURNT-OFFERING AND THE OTHER FOR A SIN-OFFERING — Scripture puts it (the עולה) first only by way of mention, but so far as offering it is concerned the sin-offering precedes the burnt-offering; thus do we learn in the Treatise Zevachim 90a, in the chapter commencing כל התדיר .

And the priest shall make atonement for her, and she shall be clean. This atonement is for the primordial sin of Eve that caused her the pain of childbirth, and in her pain perhaps she spoke harshly toward Heaven saying, “’If so, why am I’ pregnant with toil and suffering?” And proof of this is from what is written, and she shall be clean from the source of her blood — from that source that was opened for sin and impurity, for it [the sin] caused her all this, namely the sin of Eve as mentioned. Also, the language of damehah [her blood] includes the sin, from the expression their blood is upon them (Leviticus 20:27).

וכפר עליה, for during all the days that she had been excreting blood her thoughts had been preoccupied with the phenomenon of semen, etc, and she had therefore not been in a fit state of mind to enter the precincts of the Temple and offer sacred matters.