The doctor has the right not to perform a service - assuming by him doing so the patient is not in danger.
After all they do make you swear the oath....
Well anyhow, as long as alternative practitioners are available.
However, once you remove it from the individual and go towards the institution....
See the deal here?
And to remove the misogynist aspect:
Scientology does not believe in mental illness...
Should your scientology believing healthcare provider be allowed to scratch anti depressants or other medications for mental illness off the list of provided services?
This Hippocratic Oath:
I swear by Apollo, the healer, Asclepius, Hygieia, and Panacea, and I take to witness all the gods, all the goddesses, to keep according to my ability and my judgment, the following Oath and agreement: To consider dear to me, as my parents, him who taught me this art; to live in common with him and, if necessary, to share my goods with him; To look upon his children as my own brothers, to teach them this art; and that by my teaching, I will impart a knowledge of this art to my own sons, and to my teacher's sons, and to disciples bound by an indenture and oath according to the medical laws, and no others.
I will prescribe regimens for the good of my patients according to my ability and my judgment and never do harm to anyone.
I will not give a lethal drug to anyone if I am asked, nor will I advise such a plan; and similarly I will not give a woman a pessary to cause an abortion.
But I will preserve the purity of my life and my arts.
I will not cut for stone, even for patients in whom the disease is manifest; I will leave this operation to be performed by practitioners, specialists in this art.
In every house where I come I will enter only for the good of my patients, keeping myself far from all intentional ill-doing and all seduction and especially from the pleasures of love with women or with men, be they free or slaves.
All that may come to my knowledge in the exercise of my profession or in daily commerce with men, which ought not to be spread abroad, I will keep secret and will never reveal.
If I keep this oath faithfully, may I enjoy my life and practice my art, respected by all humanity and in all times; but if I swerve from it or violate it, may the reverse be my life
Yeah, I don't think you want doctors following the Hippocratic Oath as much as you think...