Why does an inductor block AC but allow DC?

While it is true that an inductor opposes the flow of an alternating current, it does not necessarily 'block it'. The quantity that opposes the flow of an AC current is the inductor's inductive reactance, expressed in ohms. Inductive reactance is proportional to the frequency of the supply voltage and, at 50 or 60 Hz, the reactance of a transformer's winding is relatively low (although very much higher than its resistance) and, while this acts to limit the amount of current flow, it certainly doesn't act to block that flow.