Why do humans swing their arms while walking?

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I think the reason that swinging arms helps in gaining forward momentum seems to be the right one. I myself tried it. I took some weights in both hands and tried walking back and forth. One can really feel the forward momentum. I also tried with weight in only one hand.
 
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Lotta deep thought here, perhaps swinging arms could just be natural propolsion?, like evolved fins, and we didn't the dorsal on our spines anymore
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Very old thread but I don't think I've seen this possible explanation mentioned..

Your legs aren't directly below your centre of mass, they are offset to each side. So as they move backwards and forwards conservation of angular momentum (about the vertical axis) means they apply a torque to the upper part of the body. It's difficult to see how that torque can be resisted without swinging your arms in counter point (eg left leg and right arm forward together).
 
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