I have a textbook that details the designing process of a common emitter BJT amplifier. When designing the biasing point, the text says to set the bias collector current so that half of the supply voltage is dropped across the resistors and half is dropped across the transistor. For example, if we had a supply voltage of 10V, we would assume that at the middle point of the load line there would be 5V across the collector-emitter junction and the other 5V would be distributed across the resistors. This supposedly gives the highest room for the signal to "swing" when input is applied.
But how does this make sense, since usually the output is taken to be the voltage between to collector and ground? So wouldn't we want to bias so that the voltage across the transistor AND the emitter resistor is equal to half of the supply? What am I missing here?