Here's a way of thinking about what's going on.
Consider a large mass, like the Earth. That mass curves spacetime in the vicinity of the Earth. A small object, like a satellite, simply moves completely freely in a "straight line" (i.e., geodesic path) according to that curved geometry. The curved geometry is such that those geodesics are just the satellite orbits that we see. In other words, the satellite isn't affected by any "force", it's just moving in a straight line in a geometry that happens to be curved, so we see it doing circles around the Earth.
It's exceedingly neat: in John Wheeler's great phrase, matter tells spacetime how to curve, and spacetime tells matter how to move. No forces required! Of course, after the fact you can tack on a notion of "force", but it's in no way fundamental.
Same thing is going on with projectile motion here on Earth.
Once you internalize this point of view, the statement about holding your arm in place becomes a lot clearer. The "natural" force-free thing your arm wants to do is to move along geodesics of spacetime, which means falling toward the Earth at an acceleration of g. But if we exert a (muscular) force to keep it up, then we can hold it in place. In short, in this point of view, forces are things which cause deviations from geodesic motion.