This reminds me of Monty Python and the Holy Grail:
King: Old Woman!
Peasant: Man!
King: Sorry, Old Man!
Peasant: I am 37.
King: What?
Peasent: I am 37. I am not old.
King: Well I can't just call you Man.
And they go on about not asking the peasent his name and blah blah blah.... Anyway maybe the Nazgul did know Arwen's name so he called her elf but he couldn't just call her elf so he called her she-elf not knowing proper manners.