In most states, when the topic is reproductive issues the patient is the primary decision maker regardless of age. So in your example, the 14 y/o female is her own decision maker. She does not have an obligation to tell her parents and in most states it is unethical and illegal for the healthcare provider to inform the parents without the patients consent.
With that being said, the most appropriate answer would be to respect the patients wishes, but encourage her to discuss these issues with her parents or other adults that she trusts. The physician could also offer to be a mediator in this conversation if the patient so desires.
Depending on how you interpret ChiDOs post, what they are recommending could be borderline unethical.
"I would also approach the parents and ask if they talked to her about these kinds of things since she's older (basically, maybe give them a push to talk to her)".
It is unethical to approach the parents and hint to them that they need to talk to their daughter about reproductive issues if by doing so you are implying that the patient brought the issue up with the doctor. The acceptable way to go about this is to make a general recommendation to the parents that given the childs age and maturity, now would be a good time to discuss reproductive topics, withOUT implying that the patient had already discussed this issue with the doctor. In general, if you feel like you are sneaking around technicalities, what youre doing is probably unethical.
Here's another angle to this question, if giving birth control is against your own morals as a physician, you are required by law (in nearly all states) to refer her to a healthcare provider that WILL provide her birth control (obviously unless it is medically contraindicated).
Just remember to always do what is in the best interest of the patient. As a premed student, experienced interviewers shouldnt ask you questions about medical ethics, which is considerably more specific than general ethics (these questions are fair game).
-senior medical student / admissions committee interviewer / plus course in medical ethics & lots of exposure to clinical medical ethics