Even the best photographer doesn't necessary end up as a 'pro'. The other half of the job is selling your work. And if your not good/hard/tough enough to pull that off (stick by your price, advertise, knowing you can pull a assignment of), you won't make it either.
The term professional is easy to understand if the "name" of the profession is interchangeable.
A person who races their car on the weekends isn't a professional race car driver.
A person who plays baseball on the weekends isn't a professional baseball player.
A person who paints their bedroom isn't a professional painter.
Owning a camera and making a couple of bucks does not make you a professional photographer.
Just because I can install a toilet, it doesn't make me a plumber.
Now being a professional photographer doesn't mean that you are better at taking pictures than amateurs, it just means that you earn your living with a camera.
I believe in the strict definition of the 'professional' as one who makes money from his work. Therefor the 'amateur' obviously would be one who doesn't make money. However I also believe being a 'professional' is not necessary a measure of 'quality' but the assumption 'quality' must be there otherwise he wouldn't be making any money or not very much money. On a personal level I don't even like to call myself an 'amateur' as this imply a level of proficiency on the same level as the 'professional' with the only difference being one makes money and the other does not. At the current point in my learning curve 'amateur" or 'professional' is a level proficiency I can't and do not claim. The best my humility would allow me to say about my own work is 'I'm an interested party' somewhere between, just 'starting out' and 'amateur' ...
I agree totally with Jan.
The definition is quite clear to me, when you earn your living with it, then you are professional. In my opinion it is not necessarily a proof of quality. I did see some wedding album made by a "Pro" that was not really good. Although usually the Pro's do indeed do a much better work, surely because they get a lot of practice...