Things You can Do with Rope

Tug others along

Tie things down

Magic tricks

Climb

Swing

With a fulcrum, increase your leverage

Cross it at the finish line

Make a net

Cut it to set things free

Tug of war

Measure

Create a barrier

Knot it up

Burn yourself badly (ouch!)

Cross impossible ravines

In short, you can lead with it.

Just like leadership, each of these things requires you to put some tension on the rope.  And just like leadership, you can’t push anything with it.