Oh! Oh! What was it? We had this problem in the design course. If I remember right you have to use the menu buttons (no keyboard shortcuts) and you it's a different option from copy/paste...it's <something else>/paste, or <something else>/<something else>.
I vaguely remember that it may have been "cut" instead of copy, to copy. Just one more reason I hate Eagle.
This is for schematic copy. If you are trying to copy a component from the library so you can modify it to your needs, it's a lot weirder. It's like you have to make another pinout set for the component and then modify that...I don't even remember anymore it was so convoluted to me.