As far as I'm inclined to agree, that causation can't be easily defined, I believe that your cycling argument is incorrect. Not only because of what the @dentalperson wrote below (they are completely right that there is a crucial difference), but also because it doesn't follow the human intuition on causation.

I understand the sentiment though. Causation should imply correlation at least on a "direct" level. Pressing the gas pedal correlates with the higher speed of the engine, not the vehicle speed. I believe the problem lies in our ability to detect the correlation. Sometimes, the correlation may go undetected (as in the case, when we ignore the engine speed in the vehicle example). I would be very happy to hear a stronger argument against "causation -> correlation" :)