You explain the reason why this is inadequate rather nicely in the rest of your post. Simply saying "I want to help people" is fairly trite and non-specific. A lot of professions are in the business of helping people. Why not be a firefighter, or a policeman, or a teacher, or even a customer service representative? What is it about medicine that makes it the best profession in which to serve others?
I agree right up until your final sentence. That framing of the question leads to the same inadequacies you mentioned at the beginning--any answer will be equally vulnerable to "A lot of professions are in the business of X." Flipping the question around gets to a better answer: what about medical service makes it the best for you?