Several weeks back, I read an article that called the quote in question "absurd." The argument was the oldest profession is hunting, as we have no evidence of hunter-gatherers ever engaging in prostitution, but we have plenty of evidence of them hunting.
I've spent a few minutes googling and unfortunately can't find the article again. But I'm not sure I agree with the article's reasoning. Does hunting so you don't starve really count as a profession? I feel like a civilization needs to exist for a profession in the modern sense of the word to exist, which would rule out taking hunter-gatherers into consideration.
What is the view on this from a historical standpoint, though?
Follow-up: If it's not a fact, where did the quote originate?
I wrote a short answer to a somewhat similar question here, so I'll just copy-paste and elaborate on it.
To answer your question you'd have to define "profession". The term is open to interpretation, but thinking of it in terms of a task being performed by a "professional" - an individual performing a task (often, but not necessarily requiring training) by which he/she comes into possession of some means of exchange which can be traded for other necessities - may be a good place to start. Thus someone doing a specialised job which takes up so much time (either to train for or perform the task in question) as to exclude subsistence on an individual level might be termed as having a profession.
What would be the prerequisites for society to allow for such specialisation? I'm not certain what you mean by saying that "civilization needs to exist". Is the existence of agriculture (i.e. post-hunter-gathering) a prerequisite for civilisation? It's a commonly held view that hunter-gathering or subsistence societies were locked in some form of constant struggle for survival, with people living in unimproved caves or crudely constructed shelters while living from day to day. There is plenty of archaeological evidence accruing to show that this view is largely a fallacy, and that elaborate societal structures and economic surpluses (allowing for investment in different fields of life - task specialisation, improving standards of living etc) predates the introduction of agriculture.
In short, hunting may indeed be a profession, but only under certain conditions. In most pre-agricultural societies hunting would probably not have been a full time job - at least not for the vast majority of people - as these would have spread their working hours over a range of different activities centered around subsistence. There may have been dedicated (and thus "professional") hunters, but if so they were in all likelihood the exception rather than the rule.
Several suggestions for what task might be termed the title of "oldest profession" have been advanced, but I'm not aware of any good evidence suggesting prostitution should be it. Instead, a good contender for the first task specialised enough to warrant using the term "professional" is that of flint knapping. This is taking us far enough back in time to be technically outside the scope of academic history (which is largely concerned with the study of written sources), but here goes. Flints and other hard, flakeable minerals became the preferred materials for making tools across most of the populated world during the paleolithic ("early/older stone age"). The earliest known crafted stone tools are hand axes found in Kenya and dating back over 3 000 000 years, with more elaborate - and famous - examples coming out of Olduvai gorge in modern day Tanzania, dating back approximately 2 000 000 years. These early examples are very simple tools, but over the millennia they become more and more elaborate. In Eurasia the most advanced examples of crafted flints turn up in the neolithic ("younger stone age" - approx. 10000BCE-2000BCE). These are such complex creations that it has been estimated by modern experimental archaeologists that building up the knowledge and skill to make them would have been more or less a full time profession. The neolithic (or possibly even mesolithic - "middle stone age") flint knapper would thus seem to qualify as the first professional expert which we know must have existed.