Why is there only 1 out of 2 wires ‘live’ in a home A.C. electricity supply despite the fact that it is ‘alternating’?

Neutral wire is not behaving "like alternating current." It is just a return path for whatever current the live wire is producing. If the live wire were DC, the neutral wire would carry DC current. But, since the live wire is AC, the neutral wire is carrying AC current. The neutral wire provides a stationery frame of reference around which the live wire "alternates." Any potential difference is measured between two points. So, if the neutral wire would also "alternate" like the live wire, the potential difference between the two would stay constant and the connection between live and neutral would become DC instead of AC.

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