Doctor is a very hard job

(Grammar Questions I Couldn't Answer)

Students were doing a presentation on jobs, and afterwards I gave them delayed correction on any grammar errors I picked up.

One sentence was "Doctor is a very hard job."

The sentence struck my native speaker intuition as wrong, but why?  Was it missing an article?  But "A doctor is a very hard job" sounded just as bad, if not worse.

During feedback, I gave alternative ways of saying the sentence--e.g. "Being a doctor is a very hard job" or "A doctor's job is very hard" or "The job of doctor is very hard."

But I was never able to explain to the student why "Doctor is a very hard job" was wrong.   And in fact the student became more confused than before.  "I thought that since doctor is already a type of job, I wouldn't need to say 'the job of doctor' " she said.
And I was unable to explain it to her.