The Mishnah (1:4) discusses cases where one must bring a korban, yet the korban cannot be consumed. The two cases brought are if a woman miscarries but there is a doubt regarding whether what she delivered obligated her to bring a korban (normally required after a woman gives birth). The second case is where two women miscarry, where one's delivery would require her to bring a korban and the other's would not, yet the two deliveries got mixed up.
Normally, if required, she would need to bring a pair of birds, a chatat (sin-offering) and olah (fully burnt offering). The blood from the chatat is cast on the mizbeach and the rest of the bird is given to the kohanim to consume. In this case, where the obligation is doubtful, the chatat is still offered, yet the bird is treated like an invalid korban and burnt. This is because, if the offering was not required, then the bird is considered like a regular bird that was not given a valid shechita and cannot be consumed. Regarding the olah however, since they can be offered voluntarily, she can stipulate that if she is not obligated to offer the olah, then it should be considered a voluntary offering.
R' Yossi in the Mishnah disagrees regarding the second case, where the deliveries of the two women got mixed up. He explains the each of the women would only be required to bring their own "doubtful" offering if they parted ways. If however they came to the Beit HaMikdash together, then they can present a pair of birds and the kohen can stipulate that they are to be offered for she that truly requires them. In that case they can be offered as certain offerings and the chatat can be consumed. What is the basis of this debate? Why do the Chachamim not accept R' Yossi's solution?
The Griz1 provides the following answer in the name of the Grach. The Gemara in Nazir (29a) asks how a yoledet (a women who gave birth) or zava can offer a korban, if the obligation to do so is in doubt. Note that a source is necessary considering that if she is not obligated, a regular animal is being slaughtered in the Beit Hamikdash which is normally prohibited. The Gemara cites the pasuk that connects the korbanot of a male and female -- "concerning a person who has his flow, whether man or woman" (Vayikra 15:33). The Gemara learns that just as a male must bring korbanot in the case of a doubt so too must a female. In other words, just like if a man were to have a doubt regarding a prohibition that is punishable with karet, the Torah requires him to offer an asham talui, so too a yoledet or zava whose obligation to bring a korban is in doubt, must also offer the chatat bird offering (even though it is not consumed).
The Grach explains that the asham talui is a definite korban obligated by the Torah. In other words, despite the doubtful origin, as long as the doubt is not resolved, there is a clear obligation to bring this korban. The Chachamim argue with R' Yossi since our case of safek chatat ha'ohf (a chatat bird offering brought in a case of doubt) is learnt from the asham talui. They therefore understand that each of these ladies has an obligation to bring their own korban. Recall that R' Yossi maintains that bringing the korbanot together would resolve the doubt, thereby allowing the korbanot to be considered definite for she that truly required it. According to the Chachamim however, since they are each [obligated]{.underline} to bring the safek chatat ha'ohf, offering the pair together will not discharge them of their obligation.
1 Mechusarei Kipurim 1:5, cited by the Yalkut Bi'urim Metivta, Keritut 7b.
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