TAZRIA
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Why is a bris on the eighth day?
It says in the Chasam Sofer that he once observed a doctor with nurses tending to a patient who was bleeding profusely. No matter how much they tried to stop it from bleeding, it wouldn’t stop. Then the doctor sent out all the nurses, and he was able to stop the bleeding quite rapidly, with ease, all by himself. The Chasam Sofer asked him how he did that? The doctor responded that he speculated that perhaps one of the nurses had their time of the month and so when he sent them out he was able to control the situation with his patient. The Chasam Sofer was blown away and asked for an explanation. The doctor said that Dam is moshech (draws) other blood. so as long as this nurse, whichever it was, with her cycle, was present, it would be impossible to stop the patient’s bleeding, so he had them leave the room.
After this incident, the Chasam Sofer said that this can perhaps be an explantion in why a bris mila is on the eighth day after birth. Because the mother must keep 7 impure days min hatorah after giving birth to a boy. After 7 days, there is no more Dam, so she can be toivel, and she’s tohor. On the eighth day you can do the bris because there is no more sakana to the baby, since there’s no more Dam Nidah from the mother.