Keritot, Chapter One, Mishnah Five
Todays mishnah lists women who do not bring a childbirth sacrifice.
The following do not bring a sacrifice:
1) A woman who discharges a sac filled with water or with blood or with pieces of flesh;
2) Or if the miscarriage was in the shape of fish, locust, unclean animals or reptiles;
3) Or if the miscarriage took place on the fortieth day [after the conception],
4) Or if it was extracted by means of a caesarean section.
a) Rabbi Shimon declares her liable [to an offering] in the case of a caesarean section.
Section one: This sac is not considered to be evidence that the woman gave birth, and therefore she does not bring a sacrifice.
Section two: These shapes are not indicative of a human fetus and therefore she does not bring a sacrifice. We should note that there might be some ideology in effect here. In mishnah two Rabbi Meir said that a woman who gives birth to a fetus in the shape of a beast, wild animal or bird is obligated. These were all kosher animals. They are also the animals that require shekhitah (slaughtering) in order to be eaten. Todays mishnah refers to living things that are either of a lower form (fish and locusts) or are not kosher (unclean animals and reptiles). Perhaps it is an ideological statement of Rabbi Meir that dictates that humans look like the former, kosher animals of a higher form, but not the latter.
Section four: According to the rabbis, the fetus is not considered to come into existence until the fortieth day. A woman who miscarries before that point is considered to have discharged a sac full of water and she is not liable for a sacrifice.
Section five: According to the first opinion, a child born through caesarean section does not make his/her mother liable to bring a sacrifice because this is not really birth. However, Rabbi Shimon holds that she is liable.