Just imagine, the Earth rotates at 1,000 mph eastward!
Moreover, the Earth is making one full rotation per day. It means that if you were standing still at the Equator, you’d really be moving East ±1,000 mph (±1670 kmh) relative to the Earth’s axis.
At first glance, it would seem like flying West would be faster, since the Earth is rotating underneath you, but this isn’t exactly the point. When you think you’re flying West, you’re really flying East: you’re just moving slower than the rest of the Earth.
Sounds confusing? This brief animation from MinutePhysics should help you figure this out.