I was reading a book, called "The 250 Biggest Mistakes 3rd Year Medical Students Make"
They need to know who you are and what your status is. You are NOT a doctor, regardless of how hard you are working to become one. Student Doctor implies that you are a Doctor, and are also a student. A doctor taking clarinet lessons could be called a Student Doctor. You see?
The point is, Medical Student is the proper way to identify yourself because you aren't a doctor.