Going back to HFD's original question - the key is that even when the motion is between points at the same lattitude this is still motion on the plane from those points perpendicular to the axis of rotation of the earth. Imagine the earth as consisting of many thin discs - each one is like a rotating turntable. Its motion on this plane that results in the coriolis force.
The coriolis force on moving air masses is zero at the equator because the force acts in the plane of the disc: at the equator this is vertical with respect to the earth's surface.
Explanations that talk about simply the tangential velocity being different at different lattitudes (as in most PPL text books) are not complete enough to answer HFD's student's question.
my brain hurts now...
H
Edit to add: agree that the maths isn't appropriate for students (or me for that matter...)