The negative, ground, is normally connected directly to the frame which then makes every other part made of conducting material connected to the frame, a grounded piece. Any hot, positive, wire only has to directly touch any of the grounded parts to get a short. Touch a hot wire with a screwdriver that is against the engine case and get a short.
With the ground removed from the post you can not get a short even if you put a wrench from the + post right to the frame. You would have to do that and reconnect the ground at the same time.
With the ground connected, all it takes is to have the wrench you are using to remove the hot ( + ) side terminal make contact with anything grounded to get a complete circuit and a short.
While removing the ground your wrench can touch the frame or any other chunk of metal and you are only touching ground to ground so no complete circuit, no short.
This short tutorial is not meant for the guy who can't resist laying his wrench on top of the battery, right on the posts. He will never understand. And then there are those silly Brits who used to do it all backwards with " positive earth" stickers. No wonder they drive on the wrong side.