AC Current confusion
Having a current flow does not make a terminal "live". Having the ability to deliver a stinging electric shock might be more a recommendation for calling a terminal "live". This means you have to distinguish between voltage and current.

Clearly, on a simple single phase AC generator, current flow is the same on both wires and if you touched one of those wires you might not feel anything until one of those wires became grounded (as per normal electricial regulations). Then you could call the ungrounded terminal "live" and the grounded terminal "neutral".