It actually helps us use _less_ energy while we walk:
https://www.reuters.com/article/us-arms/scientists-find-a-reason-for-arm-swinging-as-you-walk-idUSTRE56S15L20090729
Swinging arms in an opposing direction with respect to the lower limb reduces the angular momentum of the body, balancing the rotational motion produced during walking. This puts less stress on our leg muscles to maintain momentum and balance, which reduces overall energy expenditure.
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