Symbolic links, why doesn't this work:
Alternatively, you can do

ln -s ~/x/y ~/Desktop/


(note there's no slash '/' character after ~/x/y/).

I think the error message is not the most informative, but I understand it as that if you're putting a trailing slash, you're referring to the content of your directory (in this case ~/x/y), but if you omit it, you're referring to the directory itself.