I'm not entirely sure, but should "Professor" possibly be capitalized because it's referring directly to the person by their title (proper noun)? I think this might possibly prevent some of the confusion people are having.
For example, compare: "You're a very smart mom" with "You're very smart, Mom." In that case, the capitalization is part of what differentiates the two sentences in English, along with the article and the comma. I might be very off regarding whether "professor" is considered a name and/or title in this sentence, though.