In my answer to a similar question, I said that they way to model activities that should be executed at a given time is to create an actor called 'Scheduler' which is more of a placeholder and does not mention a technology. The idea is there has to be some person or component whose responsibility is to monitor the time and then initiate a particular use case. The use case say 'this use case starts at time X' depending on the needs of the use case. Yes time is a factor that can be modeled but the way the instructor is going about it seems a stretch to me because time itself does not care what happens when, it just is. He is over generalizing in an attempt to fit all types of use cases into his concept of modeling.
In the posited discussion with the instructor, I would ask, "Is time itself - no other mechanism, person, or software - the entity that acts upon the system?" The obvious answer being 'no' but the idea is that there CAN BE an arbitrary actor that a) can measure time, and b) knows that certain use cases are sensitive to time.
I do like the article in @Igor's answer as it really covers much of the issue with making Time a primary actor.
Actors are usually represented by some sort of noun so maybe a compromise is to use a clock as the actor instead of capital-T 'Time'. Like other posters, I agree that you are unlikely to convince the teacher but it is worth having the discussion because it helps to understand how he thinks about modeling in general.
Although I realize it is too-late for the class which generated this question, I posting this answer in hopes of helping others who have come across the problem of modeling time in a use case, or, encountering a professor who has their own opinion on how to model using UML use cases.