The smart alecky answer is that the solution of the wave equation with the stated boundry conditions requires it. It is the unique solution to the problem. I know that doesn't help very much, but if you're interested in the mathematics I can recommend:Why does a wave reflect when it meets an impedance discontinuity? And why is there a 180 degrees phase shift of the reflected wave when the transmission line finished with short circuit and no phase shift when the far end of the line is opened?