How can an inanimate object create a force?
In this particular instance, you don't actually need to think of the situation in terms of reaction forces.
What you have is leg muscles contacting and by means of a ligament around the outside of a joint extending that joint. Your muscle is providing all the force.
That force acts to extend the length of you body. In space, your body would extend in two directions and your centre of mass would remain at the same position in space. On the ground, you have your feet in contact with the ground and your hands in contact with a rock - so the force is exerted equally on your feet and on your hands (you can feel this in both those parts).
What happens next is a question of which object, rock or ice, provides least resistance. If the rock has a large mass it will not move as easily as your feet do on ice.
This is really a horizontal analogue of what happens vertically when you jump. You don't remain still and propel the planet down away from you because it's more massive. It's the work done by your leg muscles that propels you upwards - the planet didn't provide that energy.