You are quite correct, Extemp, in that a true "profession" is an occupation requiring special training in the liberal arts or sciences, especially one of the three learned professions (law, theology or medicine).  Newer "professions" may be added to that narrow list, engineering and accountancy, for example.  

However, language and its usage is something that is a living thing, and so people often ask the question these days "what is your profession?", which in fact they may really mean "what is your occupation?".  

It's easy to get bogged down in semantics, and the questioner didn't intend us to do that, but thank you for pointing this out.