The Earth's rotation is indeed fast, but it doesn't cause us to feel like we're being hurled through space because we are rotating with the Earth. The ground beneath our feet, the objects around us, and the air around us are all moving at the same speed, so there is no relative motion between us and our surroundings that would make us feel any effect of the rotation.
Additionally, the rotation is a smooth, constant motion, so there is no sudden jolt or sensation that would make us aware of it. In everyday life, we don't typically experience changes in our motion, so our bodies and minds don't register the rotation of the Earth.
It's similar to being inside a car that's moving. If the car is moving smoothly, you may not realize it's in motion unless you look out the window and see the scenery passing by. Similarly, we don't feel the rotation of the Earth because we are so used to it and everything around us is also rotating at the same speed.