Why does it take twice the distance to move the pulley?

Note: even if the rope does not slide and the pulley rises so much, the ropes on both sides should also rise so much. When the rope slides, the rope on the right side naturally has to rise twice as far, once to offset the length sent from the left and once to offset the rising height of the pulley.

So the height of the rope on the right side is twice as high as that of the little star.