disassociating related entities requires delete access
If you have a module with manually added associations, such as documents, you can select entities to add, then you can hover over them to get the trash can icon to disassociate them. The problem is that if you don't have delete rights to the target module you don't get the trash can to allow you to unlink an item. It really shouldn't be the same operation as delete because you are not deleting the object, just unlinking it.