It seems to be quite common for ethics courses taught by philosophy departments to begin with some discussion of metaethical issues (usually concerned with relativism and subjectivism). I have found over the years that I am vehemently opposed to this, for reasons similar to the reasons why I would be vehemently opposed to starting an Intro or undergraduate Logic course with the theory of fallacies:
(1) It is an improper place to begin, simply by the nature of the topic.
(2) It involves treating a very advanced topic as if it were a foundational and elementary one, to pedagogical confusion.
With regard to (1): Metaethics is meta -- which is to say, it is a reflex discipline, involving a reflection on other fields. It is impossible to do it coherently unless one already has in hand something with respect to which it is meta. No one can properly assess any of the topics discussed in metaethics unless they have a reasonable degree of understanding about the field of ethics on which metaethics is reflecting. Before you are in a position to evaluate metaethical positions, you have to know what these positions would have to explain or explain way, and why -- which is to say, you need to know something about families of approaches to ethics, examined with respect to important, specific examples. Students are regularly thrown into debates about what ethics is doing when they haven't looked at enough ethics even to understand what people think ethics might be doing.
This ties into a related problem: insufficient motivation for the discussions. Torn away from the ethical questions that has led people to ask these metaethical questions in the first place, metaethics looks like a field of random and arbitrary questions. To understand why the questions are raised (and can be taken seriously), one must understand how they arise to begin with.
With regard to (2): Metaethics by its very nature deals with more complicated and difficult questions than non-reflective ethics. It deals with epistemological questions that need to be placed in the context of broader epistemological concerns; it deals with metaphysical questions that need to be placed in a broader metaphysical context; it deals with linguistic questions that need to be related to broader questions of meaning. It is an advanced topic, not an elementary one; it presupposes, rather than leads into, the essential building blocks of the major ethical approaches.
Now, of course, with regard to both of these concerns, people are going to say, "Well, it's relevant in this or that way," but of course it's relevant, just like set theory is relevant to everything you are doing when you are doing arithmetic, and you can re-describe everything in arithmetic in set theoretical terms; that doesn't mean that it's where you start in teaching it. You need to start with something that people can use; only then do they have the materials to engage in the 'meta' thinking. And, yes, of course, it may well be that in the course of teaching ethics it will make sense to touch on this or that metaethical point, but (1) this should arise out of the teaching of approaches to ethics in a natural way, not be shoehorned in as the starting point; (2) it should arise occasionally, i.e., in a piecemeal way as naturally demanded by the actual subject you are discussing; (3) at the level of an Ethics, as opposed to a Metaethics, course, you are almost always going to be raising these issues as questions for further thought rather than as discussions in their own right, and it should be handled in a way that recognizes this.
Thus an Ethics course should just stay focused on normative ethics and applied ethics. (Although I've noted before that there are problems with how applied ethics is often taught, as well.)