Where do I start? Hmmm.....
First of all, abortion is a natural process. Dead baby in your womb? Miscarriage? Those are abortions. Usually the result of somekind of malformation occurring (like, if there's a deficient chromosome, or defective gene that causes the whole embryological development to stop or go totally awry). Plenty of miscarriages, believe it or not, are resultant from the baby having Down Syndrome (having a third Chromosome 21).
So it's not like abortion is some aberration that modern humans have invented to make life convenient. It's a natural process of our bodies deciding that this one isn't gonna work.
"That bread your baking in the oven isn't gonna cook right at this temperature...so start again, bish"
Also, abortion has been going on for hundreds of years, if not longer. Chemically-induced abortions have been occurring for hundreds, maybe thousands of years. I've read papers in my history classes in undergrad of women drinking cocktails that would induce abortions in the early days of the Ottoman Empire.
So that should dampen the argument about it being something recent, and something that is being held down by religion. The courts would sometimes decree the woman to drink the cocktail, and the Ottoman courts were all religious (whether the court was Christian, or Muslim, or Jewish). It just wasn't as common b/c extramarital sex was probably less common than it is now (a product of the culture moreso than religion).
Now, if we're to speak on the ethical duties of a medical practitioner, well, the idea of "Do no harm" calls under the ethical principle of Nonmaleficence, where the concept of do no harm is philosophically utilitarian. Thus, if the benefits of an intervention for any reason outweigh the risks, a patient may make an informed decision to proceed (most surgeries and medications call into this category).
If a patient desires an unnecessary procedure (like an abortion where her health isn't at risk), the physician really only has to understand the patients concerns and try to address those concerns. The physician will discuss with the patient why they want to do it, and if they understand the risks and consequences of their decision (informed consent of the patient). If the patient understands, and is over the age of 17, then the physician will proceed. If they are under the age of 17, then the parents are brought in to provide consent to the physician, and have to be notified at least 48 hours prior to the procedure taking place (the age of consent may vary from state to state)
The physician's first duty is to his/her patient. And in most cases, that's the patient who is pregnant. Unfortunately, the fetus comes second. The physician will take every precaution to make sure the fetus is healthy and growing according to standard developmental milestones, but it's always the health of the mother that comes first.
All that said...if you don't want a surgical procedure to take the fetus out, when you have an abortion, the doctor's gonna give you two drugs: misoprostol and mifepristone.
Mifepristone will block progesterone from working on the uterus. Progesterone is necessary for the thickening of the uteran walls and the cervix, so more sperm can't climb up, and makes the environment more hostile to another fetus developing. So by blocking it, you make the environment hostile to the developing fetus.
And Misoprostol will dilate the cervix, so that baby can pop out.
Of course, these drugs are generally given together to induce abortion within the first 50 days of pregnancy.