So I just learnt about relativity and time dilation. One of the visualisations used to explain time dilation is an apparatus contaning a beam of light moving between two mirrors. When the apparatus is stationary, the light moves a certain distance d, say in one second between the mirrors. But when the apparatus is say, fixed to a spaceship, the light beam moves in a zig zag fashion, covering a long distance $D$. The speed of light is constant. Therefore the time for light must slow down, because the distance being covered by light is greater. I have a link below which explains the visualisation. https://youtu.be/TgH9KXEQ0YU
This is what we were explained. However, why is it that the beam of light can't cover that greater distance in a greater time $t$? Why should time slow down for the beam of light?