http://www.aip.org/history/einstein/essay-einstein-relativity.htm John Stachel: "How can it happen that the speed of light relative to an observer cannot be increased or decreased if that observer moves towards or away from a light beam? Einstein states that he wrestled with this problem over a lengthy period of time, to the point of despair."
Rational thinking says it can't happen - when you start moving away from the light source and, as a result, the wavecrests start hitting you less frequently, this decrease in frequency can only be due to a decrease in the speed of the wavecrests relative to you. Yet Einstein was not a rational thinker - "I never made one of my discoveries through the process of rational thinking":
Nowadays Einsteiniana's teachers brainwash future Einsteinians into seeing a breathtaking picture: As the observer starts moving away from the light source, the frequency he measures decreases but the speed of the wavecrests relative to him remains unchanged, Divine Einstein, yes we all believe in relativity, relativity, relativity: