Cultural artifacts are quite teachable; that's generally how they are transmitted. Why would that be difficult?
How do you decide which brand of ethics to teach? Especially if your class is represented by a range of nationalities?
Look at this thread and how oblivious everyone is to the variability of the definition of ethics. We take the subject as some kind of absolute, but really we're just viewing the rest of the world through priveleged western lenses.
There's two common options chosen:
(1) broad multi-system survey rather than a single system or narrow set, and
(2) teach the system or systems most connected to the target legal system (for cases where ethics is being taught largely to create a safety buffer around legality and anticipate legality in adopting to address where legality had not yet settled.)
When you know why you want to teach ethics, it's fairly trivial to choose the approach.
Do you earnestly believe that Harvard University will be paralyzed by the choice between a modern western ethics system in which women have all the rights of men, or (to use your example) a Saudi ethics system in which women are property?
Most people in the real work are not so ridiculous that they allow themselves to be paralyzed by knowledge of ethical relativism.
The same reason that government shouldn't be legislating religion. I went to college to learn science, mathematics, liberal arts, so that I could learn to make decisions for myself-not to be indoctrinated with someone else's idea of what is right and wrong.
Edit: imagine a Saudi funded institution in the U.S. offering courses on ethics. Would you be ok with that? Why are you even sure that the particular ethics courses in Harvard agree with your own cultural norms? When you mix subjectivity with education, you get propaganda. Sure, some of it is unnavoiable because ultimately there are only so many topics one has time to learn and all educators/authors are biased humans, but the topic of ethics does not even allow for the possibility of objective treatment. It does not belong in school.