Where do you get the notion that a gas cannot push or carry an object? That is what aerodynamics is all about!

An object will keep its velocity unless an external force is applied. In the case of a projectile, the forces are gravity and air resistance. You seem to argue that the atmosphere isn't rotating with the Earth, and thus it would apply a force opposite to the rotation of the Earth. Do you have any evidence to support that notion?

A comparison. The air inside a fast moving train moves along with the train (unless it is accelerating), and if you jumped right up you would land on the same spot (not hit the rear wall). You maintain the train's and your original velocity even when you left the floor. This is also the case with Earth's atmosphere.

edit: speling and clarification.