[andrewflnr]

It doesn't really make sense until you grok how relativity thinks of events and "observing" them, and then stare at the relevant spacetime diagram for a while.

Note that the time when the light arrives from (in your scenario) Earth is not the same as "observing" it; observing is a much stronger sort of hypothetical measurement, more like assembling all the evidence in retrospect and deducing a consistent physical story. That's the story where, if stuff is moving FTL, you start seeing cause and effect reversed.

Ed: the key difference between c and your hypothetical speed of sound is that light is the same speed no matter how fast the observer is moving. Two observers both have to see a laser moving at c, even if A also sees B moving in the same direction at c/2. With your example, B can actually see the relative speed of an object moving at s as s/2.