You are spinning with the earth. You’re spinning with the earth right now. When you jump up or fly up, you don’t suddenly lose that angular momentum and the centripetal force that flings you around in a circle.
Yes, you and everything else on the earth are being flung around in a circle by gravity and your existing angular momentum which has an inertia tend to want to be conserved. You don’t feel like you’re rotating or being flung around, but that’s because you are observing from a co-rotating reference frame, so to you, you, the ground under you, and indeed the entire earth is not rotating but still.
If you were an astronaut in space observing from a comoving inertial (non co-rotating) reference frame, you would see the earth and every patch of ground and air on it spinning around its axis.
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