PMB is aware of a commonly held belief, particularly among Americans, that "real" doctors are medical doctors or physicians, and that it's offensively self-indulgent for PhD-holders to take the title "doctor." Whether this belief stems from the fact that physicians, and not chemical engineers or sociology professors, get to parade around in scrubs and expensive watches on popular TV shows, movies, and even real life, solving (or attempting to solve) a definitive set of explicitly illustrated problems with which we can all identify--or whether it's for some other reason--is not really PMB's concern here. Regardless of the cause, the belief that only physicians or medical doctors have the moral right to call themselves doctors is hogwash, based on ignorance of the history and meaning of the term "doctor" and the curricular differences between those who earn degrees in medicine and those who earn doctorates in academic disciplines. Viz:
The term "doctor" comes from the Latin "doctoris", or "teacher." Such a title has been, first and foremost for over a thousand years, an academic title. Though, coincidentally, the first academic degrees happened to be in professional disciplines, like medicine, law, and theology (theology is arguably no longer a professional discipline in the same way law or medicine are today), the title "doctor" was not bestowed simply on account of one studying medicine (or law, or theology), but because one achieved a certain level of academic distinction in a given discipline. "Doctor," "teacher," is a title of honor and accomplishment given someone who has become qualified to preside as a teacher in an institute of (higher) education. While a medieval or Renaissance "doctor" was likely to be a lawyer or a physician who also studied literature, philosophy, and the sciences (as "learned" people were "learned" people then, not specialized and divided as we are today after the democratization of education), "doctor" clearly bears no inherent relationship to the study or practice of medicine.
Presumably, after hundreds of years of linguistic slippage, the American "doctor" is more popularly understood as a physician or medical practitioner who has earned a medical doctorate, though this is at least partially the case because in the US, a doctoral degree is required to become a practicing physician. In much of the rest of the world, however, one is trained to become a physician without earning a doctorate. In the UK and much of Europe, for example, a degree in medicine (and in law) can be undertaken as one's undergraduate degree. Only after pursuing a doctoral degree (and usually submitting a thesis or dissertation of original research) does a physician become a "doctor" in the classical sense. The American-style usage of "doctor" as interchangeable with "physician" or "medic" persists in some cases, though it's widely understood that many such physicians actually don't hold doctorates at all.
As far as who deserves to wield the title of "doctor," or who gets to call themselves a "real" doctor,' the prejudice against PhD-holders is both ignorant and uncalled-for. Earning a PhD requires typically 2-3 years of coursework, examination, and/or thesis writing, only to be followed by another 3-5 years of independent research (and teaching "on the side" (ha!)) that must culminate in more or less a book-length dissertation that constitutes an original research contribution to a wider field of study. Of course, that research must be defended as the culmination of the doctoral degree, such that examiners are satisfied that the work is both strong and a viable contribution to the field. Not at all to belittle the medical doctoral curriculum, for which original research is not a requirement, but difficult and stressful examinations are; but at the very least one would be extremely hard-pressed to find evidence that earning a PhD is somehow easier or "softer" or less demanding or less "real" than earning a medical doctorate.
PMB is not in the business of telling people what to call themselves. Actually, PMB finds it tasteless to push a title--any title--in many social settings, even if you are a medical doctor. Further, PMB understands if people take exception to the use of titles in any or all situations these days, as there's an argument to be had about whether titles are unavoidably pompous, classist, etc. But the trouble starts for PMB when people unthinkingly assume not just that titles are bad, but that one type of doctor has any greater claim to the title than another, or any greater reason to identify as "doctor" in certain situations than another type. What exactly are the reasons for that differentiation, that imposed hierarchy of doctors, that gives medical doctors the right to identify as "doctor" while PhD-holders are somehow always considered insecure or pompous should they dare to take their rightful and proper title, for one reason or another?
It takes an offensive level of ignorance to think that someone who has gone through the long, grueling, and often thankless process of earning a PhD should be thought of as causing offense for simply entertaining the option of taking on the title "doctor," "teacher," which that accomplishment officially bestows upon them, and has for a millennium. A PhD-holder may not have the payoff at the end of the long road of seeing his profession dramatized amid blood and guts by the likes of George Clooney. In fact, a PhD-holder probably never had the satisfaction of taking a break from studying for exams or working late nights in the lab or brooding over a dissertation chapter to gather with friends and popcorn and have a med-school-class viewing of "Grey's Anatomy," a respite in which to fantasize about the days to come, sure to be filled with sex and heartache and, most importantly, salaries large enough to actually pay off student loans. But at the very least, a PhD-holder has the moral high ground, unequivocally, to call herself "doctor," every bit as much as, if not more than, a medical doctor, without being presumed insecure or pompous. Certainly all kinds of doctors can abuse their title and its attendant status and distinction; but the idea that only a medical doctorate deserves the option of distinction in certain situations is an insult, and should be taken as such. PhD-holders achieve a level of distinction and qualification well beyond that of BA- or MA- holders, for example, if not MD holders as well. Accordingly, PhD-holders should be expected to censor their accomplishments or to go by Mrs./Ms./Mr. no more than our ordinary holders of medical doctorates. If that's offensive to you, PMB suggests you make an appointment with your local academic historian (who, perhaps, may refer you to a specialist in the history or sociology of academic titles); they will likely have the cure for your ailment, probably for an alarmingly cheap fee.