In addition to @TrishaMeyer1's comments, I would add that you might need to turn it on at the course level.  I'm an admin at my institution and we have New Quizzes available for instructors to turn on themselves in their courses if they want to. If they want it on, they go to their course -> Settings -> Feature Options and enable New Quizzes. This will make it so they get the prompt when they create a quiz to make it a New or Classic Quiz.