The body of the valve is continually being accelerated towards the centre of the wheel, a movement which it must comply with because it is rigidly connected to the wheel. The moving pin in the centre of the valve is however free to move, up to a point, so it's inertia will tend to cause it to try to move in a straight line and not follow the movement of the valve body, and thereby spring open. The reason that the pin does not move and allow air out once the wheel starts spinning is that there is a considerable force acting on it in the opposite direction due to the air pressure inside the tyre forcing it into contact with the valve body, and being very light, its inertia is normally not enough to overcome this force. If the air pressure was very low or the rotational speed very high, you might get close to a condition where the valve opened, but I think that is extremely unlikely.