Maybe it's okay to use an article when we're not really talking about what he does for a living, like we're just explaining something or responding to a previous statement.
Person A: "I don't like it that my tree lost it leaves!"
Person B: "Well, it's a tree; trees do normally lose their leaves once a year."
Person A: "Mr. X is such a thief and a liar!
Person B: "Well, dear, he's a politician."
Yeah, I can see how there is a difference between refering to someone's job title and using the term to explain something.