Why is the gain of feedback amplifier Vo/Vs?
Vf is nothing but fraction of output voltage (Vo)  that is fed back to the input for various purposes(to increase stability for example)
Well let me take op amp example 
Think of the outer box in picture as black box and u don't know what is inside of it.
So for you what u have in hand or what u can measure  is Vin and Vout 
Amplification=Vout/Vin
Vf does it's job internally and u don't consider it while writing the gain formula or amplification formula