Now, forget about relativity for a minute. This still sounds rather...well, dumb. What would make anyone think that it IS stationary, when it's obvious that you're chasing it??
Please, take a minute and reread my previous post. It's exactly what Einstein was pondering about and directly relates to the quote from your book. Einstein may have been only 16, but he wasn't the one who first contended that the speed of light is invariant of the reference frame. That came out of Maxwell's work. Einstein realized how this seemed to contradict Newton, and hence his assessment as a 'paradox'.
What would make anyone think it should be stationary? Newton certainly would think so. I think you still have trouble keeping your reference frames straight. You are right, that this has nothing to do with Einstein's 'relativity'. However, it does have something to do with 'relative motion'. Back to your car example: If the car moves at 5mph and you walk along at 5mph, the car
appears to be stationary from your point of view (i.e. in your reference frame). That's because you stay with the car, and the car never moves away from you. In your reference frame, it looks like the car and you are stationary, and the road is moving away under your feet. You follow? This is what's meant by
"we will catch up with the light waves and so they will appear stationary;light will stand still". Read on, only if you understand this.
Einstein and Newton may now think, why should light waves be any different from cars. If we could move along with the speed of light, the wave should be always at our side, never moving away from us,
appearing stationary with respect to us. Do you follow? Only read on if you understand this.
The point is, that light is
not like car! What holds for the car completely breaks down for the light wave, according to Maxwell. We can move along with the wave at the speed of light, assuming to catch up with it, but we never will. The light wave will always be faster than us, by exactly the speed of light! Does this seem weird and paradoxical now? It sure did to Einstein.
Now read your quote again. It's exactly what I am trying to describe.