I think your difficulty visualising this is to do with ‘just kind of moving back and forth’. Although the current direction alternates with ac, you still need a complete circuit for current to flow.
If you took a single moment in time snapshot of the circuit behaviour, part way through one half cycle of the ac waveform, it would be little different to a dc circuit with a battery connected one way round. The current would be flowing from hot to neutral.
Then, if you waited half a cycle and took another snapshot, the current would be flowing from neutral to hot. The equivalent of having your dc battery connected the other way round.
Neutral sits at 0V, hot alternates between being more positive than this and more negative than this causing the current flow to reverse direction with each half cycle.
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