I remember watching a lecture by Donnie Burns once in which he stated that (and I am paraphrasing crudely) there are many excellent teachers that have never won any championship(s) and yet will contribute to the growth of young dancers in an incredibly significant manner simply because they are (a) amazing teachers, and (b) know their craft fully. More on this concept in a few sentences.
I have always been torn in the label of "Professional" especially because, and when, it was assigned to me at the age of 22 as I began teaching Ballroom. In my eyes I was a 22 year old college kid who did not know anything and was majoring in Education and English; I was in no position to be teaching dance to anyone. I had started learning it when I was 17 myself; 22 - 17 is a difference of 5, which does not a "Professional" make. And yet, here I was, labeled a "Professional Dancer" because it was, indeed, my profession (read: the means through which I made a living). I would like to think that over time I earned the title that was merely given to me. I attended lectures, conferences, watched videos, competed, and worked hard to understand my body, the theory of movement, anatomy, and the psychology and emotions of the dances I taught. I read textbooks on Latin, Standard, the Anatomy of Movement, psychology, and really on anything I could get my hands on if I thought it would improve (a) my teaching, and (b) my dancing. Ultimately it did, it all paid off, as I was seen by many in that studio as not only one of the best dancers but one of the best teachers as well.
Granted, perhaps it is easy to be "a big fish in a small pond," but here is where my opening statement of the reply comes in. I have never won Blackpool. I have never even been to Blackpool. I haven't even won at the most local competition I've ever attended. But I can profoundly profess (pun intended) that I have taught people who knew naught about dancing myriad of things about themselves, and about Ballroom. There is a difference between a dancer who teachers and a teacher who dances, and I think that this is in line with Larinda's train of thought in that we hear a term and we attribute certain characteristics or qualities to it whether they are there or not; we expect it to be there because in a sense those things are part of the definition. And yet, it is not always so.
Someone said that being a professional is a choice, and I do not disagree -- being a professional is a choice, same as being professional is a choice. The two should go hand in hand, meaning that if one is a prof. then without a doubt one should act professionally. What that entails, however, can be debated and argued as per the standards of the particular industry.
We have all, no doubt, heard horror stories of hard-sell tactics or improper behaviors between [dance] student and [dance] teacher. We then should ask ourselves, in reference and answer to OP's question, which standards do we use to determine what this particular term means. As "Professionals," are we "dancers" first and "teachers" second. "teachers" first and "dancers" second, or are we neither of those and are something else entirely? Depending on the definition we use for ourselves we will most likely manifest the behaviors, characteristics, and traits we associate with it.
I believe that a Professional is someone who knows the subject, the methodology to appropriately pass on the necessary information to those interested, and this knowledge and this methodology are both done in a respectful, sincere, and honest way. A Professional is not shady, is not manipulative, and not selfish in their behaviors and antics. But that's my definition... I strived to be a "decent human being" when I taught dance, same as I strive to be a "decent human being" now while I teach English.
Perhaps this was a little more scatterbrained than I originally intended. Sincerest hopes this post made sense.