Why output of common emitter amplifier is inverted?

In a common emitter amplifier, the base-emitter current causes a corresponding collector-emitter current, in the ratio of hFe (beta gain) or collector resistance over emitter resistance, which ever is less. Since this ratio is usually greater than one, the differential collector current is greater than the differential base current. This results in amplification of the base signal.

As you increase the base-emitter current, the collector-emitter current also increases. This results in the collector being pulled towards the emitter, with the result that the differential collector voltage decreases. This results in inversion of the base signal.