Why can a differential backup not be copy-only?
It can be specified in TSQL but the documentation states


  COPY_ONLY has no effect when specified with the DIFFERENTIAL option.


There's no need for copy only differential backups because you can just take a normal differential backup.

Taking a differential backup doesn't break anything as each such backup is cumulative and contains all changes since the last full backup. 

If you were to take a full backup without copy_only that would potentially be problematic as it resets the differential base (clears the bitmaps containing information about which extents have changed).