Sometimes your input signal is genuine bipolar AC, centered around 0V and possibly weak (uV or mv). It makes sense to continue this AC mode throughout your op amp (or collection of current mirrors and current sources). That way you can use your input signal unaltered and close to 0V. The workaround is that our power supply must have positive and negative rails (near-universal advice when building with op amps). Then NPNs turn on normally. The output stage operates normally.
We can prefer our op amp to run on a single-ended DC power supply. But then we must apply certain DC bias voltages and mix them with our inputs. We must always keep this in mind as we develop the circuit. We must account for a midway DC level running through all components. We must make an output stage that takes this into account.