I though rearward CoG means plane pitches up
So far OK.
requiring elevator input to pitch it down.
Yes, but precisely what KIND of input?
If the plane pitches up it means its nose goes up but its tail goes down. If the tail goes down what do we do to make the tail go back up? We lower the downward force on the elevator - which means less 'input. The force on the elevator is always down.
Yes, center of gravity is always forward of the center of lift in conventional (non-canard) airplane.