I don't see this question as black and white as some.
There are so many different types of photography and markets for different types of photos that the term pro or professional doesn't really apply.
For example - Ansel Adams was a fine art photographer. He didn't shoot weddings or to my knowledge even do any commercial work. Would you consider him a pro? He studied music and probably was broke for the early part of his career.
Professors at University's very often produce fine art photos or do commercial work in addition to teaching. Are they not professional photographers because they don't make photos "Full Time."
I know many photographers who earn all of their income through photography and even their work is not so cut and dry. They sell stock, make fine art prints, shoot photos for ads, or work on portraits for politicians.
Plato the Wise mentions a relevant issue in connection with those persons employed in higher education. For those holding positions at institutions granting degrees (e.g., B.F.A. and M.F.A.), sustained production of art is required for tenure as well as for advancement to the associate and full professor ranks. Such persons are artists employed at academic institutions (they hold titles of Professor, Associate Professor, or Assistant Professor) who have chosen photography as their medium.
Having met innumerable persons (not just photographers, but also artists in other fields) working in academia, I observe that they identify themselves as artists, not as professional photographers; as artists, not as professional painters; as artists, not as professional sculptors; and so forth. There is yet another nuance, then, to the apparently "easy" business of definition.
What to make of artist self-identification? Merely that, as this thread exemplifies, an absolute definition of "professional" in the context of photography (or in the context of art generally) is not self-evident, notwithstanding what may be found in Wikipedia, the dictionary, or elsewhere.
This is certainly an interesting and enjoyable thread.