I recently discovered an old Camerawork magazine from November 1977 that asked the question above, most of us have probably been asked the question many times by Police officers or other jobs-worths while out on the streets pursuing are legal right to take photographs of strangers in public places, the question in my opinion is barely worth an answer however I believe the question has greater value when we ask it of ourselves !
Anyone reading this who is motivated to create Street Photography for anticipated financial gain is heading for disappointment, some might manage to earn from workshops and lectures but this should not be seen as an income from SP as this is an income from teaching. The old adage of those that can , do and those that can't, teach might be relevant here.
I have some reservations about teaching Street Photography to anyone as I believe that "street" should be a personal vision that is best left uncorrupted by "experts" in the early days of a photographers development. I have no problem with the teaching of the mechanics of photography to newcomers but I see no value in burdening new togs with do's and don't s and visual limitations as these new togs bring fresh eyes to the party and that is an increasingly rare quality amongst seasoned street togs !
I spent many years creating images for money, I like everyone else needed to make a living, with hindsight I regret not using photography as a form personal expression earlier in my life, the conflicting demands of personal photography, commercial shoots and life in general make a balanced approach difficult to maintain.
This question of motivation is a much easier question to ask than it is to answer, the question or more importantly your answer should help you discover a lot about yourself and your relationship with your own photography.
What price are you prepared to pay to maintain your creative integrity and photographic independence ?