Q:

How do we not feel the speed of rotation of Earth?

Many people say, we don't feel the speed because everything around us including the air moves with the same speed, but I am not satisfied with the explanation. If it was so, shouldn't we feel a huge amount of resistance if we move in the opposite direction of rotation of earth? I know there's some serious mistake in my interpretation but I don't know what's the mistake.

A:

If it was so,shouldn't we feel a huge amount of resistance if we move in the opposite direction of rotation of earth?

Your movement against the rotation is relative to it.  You are still rotating, you're just rotating a little more slowly than everything else that is rotating.

