I have a course that magically duplicated itself. When I try to delete one version, it deletes both. When I make a change to once course (i.e put delete in the title), it adds it to both versions. Is it a way to break/unlink them so I can delete one?
It looks like you are dealing with a shortcut or parent object reference, as per your statement, the original object also gets deleted when you delete the duplicate.
Anyway, I would have started with activating both Structure and Content Reference Counters in the Producer. It's under View - Workarea Details. After activating them, check whether there are numbers bigger than "1" next to your course assets and the course itself. If all numbers are "1" only, and your course is on the same level in the hierarchy as the root group, we deal with the shortcut, not a reference.
In the recent SEN version deleting shortcuts has been made easy. Just select the object, and delete it. The shortcut will disappear from the topmost level, but the object will stay in its original folder.
If there are numbers other than "1," then use the Structure Reference Counter button to find out where the reference is located, and if it's safe to delete this reference - do it.
For this moment, I think you are dealing with the referenced asset rather than the shortcut.