Why does coriolis work 90 degrees to the direction of travel?

so you fire a rocket from the south pole and it seemingly veers off t the left. But why anyway? We were taught that the earth turns underneath the rocket. but the rocket was in sync with the earth when it was fired. I understood this in the clroom very well but now i seem to have lost it. it would only really make sense if the world sped up while it was airbourne. and why 90 degrees? gyroscopics?