Childbirth is one of the most amazing and inspiring events that a woman can undergo; it is a way for humans to imitate Hashem and create something new, just like He does. One would expect that after such an experience, a new mother would bring a Korban Todah (thanksgiving sacrifice); however, the Torah commands the mother to bring a Korban Chatat instead. What would compel the Torah to make the mother bring such a Korban? It seems inappropriate for the occasion.
Rav Kelman cites a Midrash, which explains that since childbirth is a painful experience there may have been a split second of extreme pain in which the mother may have thought that it would have been better not to have the child at all. Even though the mother did not mean this seriously, the very fact that this thought entered her mind is reason enough to make her give a Chatat instead of a Todah.
Nechama Leibowitz offers a different explanation. When a child is born, the mother looks at this pure and innocent child and looks at herself and what she has become. More often than not, the mother will realize that when she was born she had so much potential to become an amazing person; however, as time went on, she drifted farther and farther from that goal. The very fact that the mother comes to terms with this and realizes how little she really has accomplished is reason enough to give a Chatat to Hashem.
When a baby is born, its parents, especially its mother, start to realize how special life is. The free, nonchalant attitude that people express before the baby’s arrival is brought to a halt upon the birth of the child, when new responsibilities arise for the parents. After this maturing process, the parents realize how irresponsible and greedy they might have been. Only once the baby is born can parents truly appreciate how much their parents sacrificed for them and how much they owe their parents and Hashem for being so considerate and caring for them all this time. After the parents experience the birth and maturing process, it is no surprise that the mother brings a Chatat and not a Todah; now she realizes what it means to be considerate just like her parents and Hashem were to her.