[bramen]

I'm not sure about this analogy. You can argue that the apparent motion of the wave crests is an illusion being pieced together by our brains when we see the totality of the elliptical movements of water particles at the surface.

But at the moment when you drop a pebble into a pond, there are definitely parts of the surface which are moving and parts which are not, and the influence of the energy you introduced with the pebble can clearly be seen to spread outward over time.

Granted this doesn't map directly onto electromagnetic waves because the mechanisms involved in wave propagation are different.