In the CE amplifier the output voltage is in a inverse relation with the Ic current. When Ic increases when the input signal is swinging up the voltage across the collector resistor increases and as such the output voltage decreases (for the basic configuration Vout = Vcc-Ic*Rc).
This is not the case for CC and CB.
Miller capacitance is due to a "feedback" capacitor between the input and the output in the high frequency model of a transistor. In the case of BJT's there is no modeled capacitance between emitter-collector and as such there isn't a miller capacitance for the CB case. There is a feedback capacitor in the CC case but because the gain of such a stage is usually around 1 then the miller capacitance is insignificant i think.