Only the males sing, which has led many scientists to theorize that they croon to attract females. The hole in this argument, though, is that no one has ever seen a female whale show any interest in a male’s song.
Just because women show no interest doesn’t mean a guy isn’t doing it in the hopes of getting laid*. We just assume they’re playing hard-to-get.
*according to the Michael-from-The-Big-Chill hypothesis