In the case of the "super glued finger analogy" the finger IS the handle. You push the handle towards you by moving your hand, and that force is transferred to the bottle (and the rear of the bottle) by the handle.
Imagine there is a pencil stuck to the bottle, instead of your finger. Now turn the bottle so the pencil is facing away from you. Now you grab the pencil as you would the bottle, with your pinky closest to you and your thumb farthest from you. Now push. The bottle moves away from you (aka, "pushing the rope"). The exact same thing happens when you keep everything the same and rotate the bottle 180deg so the pencil is now facing towards yourself. You push the bottle towards yourself, in the exact same way you pushed it away from yourself a moment ago.
In the case of the "super glued finger analogy" the finger IS the handle. You push the handle towards you by moving your hand, and that force is transferred to the bottle (and the rear of the bottle) by the handle.
Imagine there is a pencil stuck to the bottle, instead of your finger. Now turn the bottle so the pencil is facing away from you. Now you grab the pencil as you would the bottle, with your pinky closest to you and your thumb farthest from you. Now push. The bottle moves away from you (aka, "pushing the rope"). The exact same thing happens when you keep everything the same and rotate the bottle 180deg so the pencil is now facing towards yourself. You push the bottle towards yourself, in the exact same way you pushed it away from yourself a moment ago.