Rachael Larimore's comment that the Hippocratic Oath mentions abortion is a little disingenuous; yes, in forbade doctors from performing abortions, but it also forbade doctors from performing any sort of surgery.

I guess it depends on your definition of "first do no harm." I don't believe an ob/gyn is obligated to perform an elective abortion just because their patient wants one, but I do believe a doctor may need to perform the procedure if the woman is dying from a tubal pregnancy, or was in a car wreck and is critical, etc. I can think of very few instances where a doctor would be obligated to perform an abortion, and no doctor has to do any elective surgery just because the patient wants one. An internologist is under no obligation to do a gastric bypass just because his patient can't lose weight, either.

for stone." Bladder stones were common in the ancient world, and itinerant lithotomists traveled from village to village, collecting their fees in advance, put their patients through gruesome procedures, and skipping town before their patients (nearly uniformly) died. That sounds more like some forms of abortion than modern surgery

Sounds more like mid-wifery - something not necessary for normal delivery and not very helpful in cases of unusual delivery

The specifics in the Hippocratic oath regarding abortions and kidney stone removal had to do with the "turf battle" at the time it was written. Abortions were thought to be under the providence of midwives, and kidney stones (of all things) the realm of lithotomists. Times change. A more modern version might disallow the treatment of dental or foot problems since these now have their own specialists, outside of medicine.

Hewing to the original Hippocratic Oath is not really something that Christians want to promote, anyway. You cannot take it and remain a Christian, really. It requires swearing an oath by pagan gods.