It goes deeper than this. The basic assumption of relativity is that all refence frames moving with constant velocities relative to each other will be experienced by an observer within any one of them as being stationary; i.e. the observer will not be able to perform ANY experiment within his/her reference frame from which he/she can conclude that he/she is moving. This requires that each observer within whichever reference frame must measure the same speed for light. If not the observer would be able to conclude that he/she is moving. Thus if you move with a speed of c/2 relative to a reference frame, you will experience the reference frame moving with you as being stationary and you will thus measure the speed of light as c; however, an observer within the reference frame relative to which you are moving with c/2 will see you catching up on light because he/she also measures light speed as c relative to his/her reference frame as well as your speed of c/2.
