I think what they mean is that the force we call gravity is an illusion that we experience because we perceive spacetime as flat. In a curved spacetime, you don't need to posit a force to explain motion due to a nearby mass - the mass curves spacetime, and objects move along geodesics in the curved spacetime. So while it would be incorrect to say "gravity is an illusion" I think it makes sense to say "the force of gravity is an illusion".
He's probably quite aware of what the intended meaning is. The point is that since we're in effect always talking about 'verisimilitudes', calling this or that an "illusion" is silly, because it implies that we didn't realize our models are just models ("You mean to tell me the Standard Model isn't a 1-to-1 mapping from reality to our brains??? NOOOOO * worldview shattered * ").
For example, the spacetime explanation for gravity is also a model, and is also likely to be an "illusion." Making note of that is theoretical physics 101... or at least it should be.
In short because things move from a state of higher energy to lower energy. Not subduing yourself to gravity would take energy in opposite direction to counteract it (or the geometric slope in this analogy). Newtonian conservation of energy is a pretty good model analogy (although isn't the same thing) and the geometric one is even better. But that's all they are, however accurate - analogies, constructed on the basis of available information and mathematical models.
Outside of that there really isn't a 'reason'. This isn't how physics works, although it's certainly in our nature to create and expect meaning and cause everywhere. Brain is bound to think in hierarchies, because that's how it's built to operate, but the universe doesn't have that limitation.
You hit the nail on the head. The real issue is that the force is not considered fundamental, because it is explained by some other model such as spacetime curvature.
I thought those seemed part and parcel. :) "I'm in the gravity well of a star" leads to "this alters the geodesic of spacetime that the I tumble down", which made me wonder "wait, why does it tumble down geodesics to begin with".
The answers seems to be "physics doesn't have to abide by your intuition or need for narratives, human"
