Why cant I use the same expression for doppler effect when the source is in motion and when the listener is in motion?

This is a common misconception that involves changes in frames of reference. In most contexts moving towards an object refers to the same physical reality as the object moving towards you (at constant speed). In the scenario we are concerned with, there's is a wave moving through space and the velocity of this motion is given with respect to the stationary air. This is the reason why in this case we can not simply suppose that we are not moving and the source it's coming towards us, the speed of the wave changes in this situation.