only Psychiatrists are "doctors"....unless you mean PHD, not MD
That's not true.
You're assuming that the term "doctor" is exclusive in some way to medical doctors.
A person with a Doctorate, say a Juris Doctor (JD) is a Doctor of Law, just like a Medical Doctor is a Doctor of medicine. An MD has no exclusivity right to the term "Doctor".
You can be both a psychologist and a psychiatrist and in both cases are a Doctor. A Doctorate in Psychology, makes you a Doctor of Psychology. A Psychiatrist is a Medical Doctor that did a residency in psychiatry.
In my opinion, if anyone has the ultimate right to be called a "Doctor", it's actually the PhD'er.
The title of "Doctor" comes from the Latin word that means "teacher".
A Medical Doctor practices (doesn't teach) medicine, hence why he is called a Physician.
When it comes to being a "teacher", PhD'ers are usually those that advance our knowledge in the various disciplines of academia and science. They are the ones that "teach" us new things, whereby the medical doctors (or physicians) simply apply the knowledge provided by those "teachers".
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