Why do I have to have administrator permissions to remove a desktop shortcut in windows 7?

This isn't just a feature of Windows 7, but previous versions too.

Desktop items can either be in the "Shared" desktop folder or the users personal desktop folder, but they are shown together to the user as a single combined desktop with no immediate indication of which location an item is stored in.

Anything in the "Shared" folder require admin rights to modify, while the contents of the personal one can be manipulated by the user as well.

On Windows 7 and Vista these are normally located:

C:\Users\Public\Desktop
C:\Users\$USERID$\Desktop

On Windows XP these are normally located:

C:\Documents and Settings\All Users\Desktop
C:\Documents and Settings\$USERID$\Desktop

I believe this is to do with how windows combines the 'all users' folders with your own.

I don't have a 7 install to hand, but on XP, the contents of the folders:

C:\Documents and Settings\All Users\Desktop

&

C:\Documents and Settings\Pricechild\Desktop

are both combined to produce what I see on my desktop. I assume it is similar to 7's method but with different paths.

The reason this is important is because you don't want users changing other users' desktops. (including the shared bit of their desktops) Thus, the 'All Users' folder will be protected and only editable by administrators (hence uac coming in to play)

So to get around this, make sure you create all shortcuts in your own desktop, rather than shared across all users in the all users\Desktop folder (or its windows 7 equivalent)