Step off a tall building and flap your arms wildly.

Unless your name is Wiley Coyote, you don't manage to fly for more than the comedic second or two it takes for the brain to realise this is impossible. Then gravity takes over.

Without wings big enough to beat on the air, and air to work against, no amount of arm-flapping will stop your fall, or change your orbit.

I guess you're basing your analogue on a swing, where pumping motions of the legs and body can accelerate the swing without outside influence.

If you study that case carefully, however, you will see that opposing forces are delivered to the Earth, via the frame of the swing. If you were in orbit, on your swing, it wouldn't work, even if the swing chains were a rigid arm. The trouble is, all parts of the system are equally in free-fall as they orbit around the Earth.

Similarly, your thought experiment doesn't work either. If you wanted to, you could build a small working model at the surface of the Earth and try it out. You'd find that the body of the device might jump up and down, but on average would weigh the same and neither go up nor go down.

(in fact, to higher order, there IS a nett force:- If the arms of the pendulums are very long, then the gradient of gravity from the Earth is non-negligible. In the time spent underneath the body when they are pulling it down by accelerating, they weigh fractionally more than in the time above the body when they are pulling it up by decelerating. This makes the body of the spacecraft travel in a fractionally lower and faster orbit than you would expect, but the difference is fractions of a mm for most practical cases, and still effectively irrelevant. The craft does NOT spiral down, and specially does not spiral up)

(Second corollory. If your body is massive, it raises tides in the Earth due to the gradient of *it's* gravity. If your initial orbit is higher than geostationary, the Earth's spin will accelerate you in your orbit. Over millions of years, you will slowly recede from the Earth, as does the Moon. If your initial orbit is closer than geostationary, you will spiral in, as does Phobos.)