There are plenty of amateurs who are better dancers than many professionals. There's no standard of ability to be a professional dancer. It's really just what box you check on the entry form (there are even amateurs who earn money dancing and teaching, so that's not always a helpful cutoff.)
Without getting wrapped around the language axle too much... I think part of the problem in our particular instance is that there aren't many dancers making a living solely by dancing in competitions. Even the ones that make some money from comps are deriving most of their income from teaching, running a studio, being a vendor, etc. Every field has its share of incompetent people, and it's true that often, the top amateurs in a field surpass the work of the below-average pros in that field. But in general, the person who does it for a living is going to put a lot more time into studying and practicing than the person who has to spend 40 hours or more a week doing something else to earn a living, and on average that will be reflected in the results. (This is putting aside vocations in which some kind of certification is necessary to enter the field at all, e.g., airline pilots. In such fields, finding any amateurs at all is rare.) And as we know, the competition sanctioning bodies have (deliberately?) done a lot of stuff recently to muddy the waters between who is considered a pro or an amateur.
I personally don't worry much about how much money the person who is instructing or coaching me makes off of dancing. It's none of my business, and it's not relevant to dance instruction as such. However, the person who meets the standards for what I expect in an instructor / coach is more likely to be someone who does it for a living, i.e., a pro. It doesn't mean I would never take lessons from an amateur, but an amateur is probably less likely to fill the bill for what I want. Whether that person is a pro or an amateur in terms of where they derive their living from, I do expect them to conduct themselves in a professional manner, because that's what I'm paying for.
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 teachingdance 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.