(1) The supply of doctors (and other health professionals) is restricted by licensing, not driven by the demand for their services.
(2) The price of health care is not determined by supply and demand, but by various regulatory arrangements and bulk agreements which often do not involve either the producers (doctors, hospitals, etc.) or the consumers (patients) of the services. So the parties who are determining the prices are the ones with the least possible stake in the outcome.
(3) The consumers of health care, patients, are almost always unaware of the cost of the services they are getting, so they have no way of knowing whether those services are worth more than they cost, and hence no way of signaling where health care is being inefficiently provided.
(4) What the US healthcare system calls "health insurance" is actually a combination of insurance and prepaid health care. Insurance is supposed to be for unforeseen costly events, but most health care does not consist of unforeseen costly events but of predictable expenses (annual physicals, shots) and unforeseen not very costly events (you go to the doctor with the flu, get an exam, and are told to rest and drink lots of fluids).
(5) Prescription drugs are regulated by a regime (the FDA) that is heavily penalized if an approved drug has any bad effects whatsoever, but suffers no penalty whatsoever for keeping helpful drugs off the market for years while they undergo "testing" and hence depriving large numbers of people of their benefits.
I'm sure there are more, but those are just the ones I came up with off the top of my head.
