My dear Calvin, I don't agree with Bharath's point that in philosophy classrooms there is a pretend doubt phenomenon. Contrary to how Bharath makes it seem, when the professor raises the doubt "Are all values subjective?" she isn't speaking for herself. Rather, she is raising a doubt which someone might raise, for example, someone who is a moral skeptic. And why is the professor doing this? Because by raising the question she is challenging the students' conception of the world, and forcing them to rethink their deepest assumptions.
But, Hobbes, there is a simple response to the moral skeptic who worries if all values are subjective. Suppose I am talking to The Moral Skeptic. Either she acknowledges that our interaction is governed by values of civil discourse or she doesn't. If she does acknowledge such values, then she isn't actually a moral skeptic; she is just saying some words without realizing that she doesn't believe what she is saying. And if she doesn't acknowledge such values, then she and I are not going to be able to have a pleasant conversation anyhow. If we can't take for granted that while talking she can't use me as a punching bag, I sure as hell am not going to be able to have a simple philosophical conversation. I will then be seriously worried for her and for myself. If I come across a real moral skeptic, my worry wouldn't be that I wouldn't be able to convince her by argument. My worry would be: what if she steals my money, or stabs me? This is a loose cannon I am dealing with! Suppose she isn't actually a moral skeptic, but is toying with the position, and seriously wondering about it. Then I would assume that she is feeling really estranged from society and must be feeling very lonely and hurt, and I would see how I can help by bringing her off the ledge of such deep pessimism. The point that a professor can't be a moral skeptic because she is a professor applies in a sense to everyone. A father who aims to be even a decent father can't be a complete moral skeptic; for being a father means being committed to guiding one's child in some ways which will help the child when she grows up. Similarly with anyone who aims to be a neighbor or a friend, or any of the normal identities we as people strive for. There is no magical person we will come across to whom we have no bonds as people, and with whom one can discuss moral skepticism as if it were a purely theoretical issue. As I see it, this settles the worry of moral skepticism. What is there to go on about for a whole semester?