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?
by Jake Hertz
by Duane Benson
by Jake Hertz
by Jerry Twomey