[masterboyz]

You have somewhat of a point, but your pivot argument can be applied to the rope too : when the rope pulls up on one end, the other end pivots down into the ground.

However, by pushing up with the pole, the leading edge in contact with the ground might dig in, making it harder to move, whereas pulling up with the rope it's the trailing edge that's in contact with the ground and therefore will not dig in, making the box easier to slide.

However, this requires the modelling of the characteristics of the ground on which the box lies, which IMO is probably out of the scope of the question. However, mentioning this in the answer might yield some extra marks