Why Power gain means the output signal carries more power than the input signal, and that extra power has to come from a DC supply. A transistor is an active device: a small base current (or gate voltage) controls a much larger current drawn from the power supply, so the signal power out can far exceed the signal power in. Passive parts have no supply to draw from, so they can never produce power gain.
Watch out A transformer is the tempting one because it can step voltage up, but voltage gain is not power gain: the current drops in the same proportion, and real transformers deliver slightly less power than they take in. Resistors only dissipate power, and a reactor (inductor) stores and returns energy without adding any.
Gain needs a power supply. Only the transistor has one plugged in; transformers just trade volts for amps.