I have a few theories.

It's possible that English is not your first language, in which case your professor actually wrote a very different question than you present here. This hypothetical question, in its original tongue a nuanced play on homonyms, generates confusion here when mistakenly mistranslated.

Another theory is that your professor is referring to something esoteric that either was mentioned in class previously or is assumed to be common knowledge. This hypothetical reference could be from literature or popular television, and its meaning would override the literal interpretation of the question.

This leads me to my third theory: the question was meant to be taken literally. In this scenario, your professor offered a simple question that would be almost impossible to misunderstand. The purpose of this may have been to provide easy points, thereby bolstering class scores, or, resulting in a desired total possible score for the quiz.

Yet another theory is that there is no correct answer to this question. Your professor may have posed it to prompt a logical or existential investigation into the calendar.

Less likely perhaps is that your professor is performing an experiment on your class. The professor may have included this question on an experimental group of yourself and your classmates. Or, there may have been variations on this question that appeared on others' quizzes.

Another theory is that your professor assumed that this question would be very difficult. In this scenario, the professor depended upon your inability to answer it correctly. It was included then perhaps as a way of ensuring a lower average score on the quiz.

Perhaps your professor accidentally included the question. Thinking his clipboard was full of another phrase, he pressed Ctrl+V and looked away, leaving behind a misplaced artifact of his diary.

Perhaps your professor changed replaced the word Friday with Tuesday on half of the quizzes. In this scenario, your professor has developed a strategy to determine whether cheating is going on in the classroom. The professor alternates test versions as they are passed out. If a student looks solely off another student's answers, they will have missed a very simple question. This will indicate that they may have been cheating.

Perhaps your professor genuinely believes that application of C. Wright Mills' "sociological imagination" changes the answer to this question. In this scenario, the professor has prompted the class to use a sociological imagination while taking quizzes in your course. Is, sociologically speaking, today Friday? If this was your professors intent, I admit that I too am puzzled by the question.

I also think that it is possible that you are making a joke.