Could the phrase also be "Nem tanár vagyok, hanem diák"? It's my understanding that Hungarian verbs already contain the subject information, or am I wrong?
The hungarian sentence didnt use the definite article therefore the english sentence also shouldnt use it. In hungarian one doesnt need to use indefinite article in this case (though it is not wrong to add it), but in english one has to use it when talking about someone being a student, worker.