Human bipedalism is awkward at best.
Basically as we walk we fall forward and use our legs to keep us from collapsing.
Swinging the arms helps maintain balance - something we don't exactly have in spades.
You can run with your arms down by your side, or with something in your arms, but you'll notice that you feel a lot less stable doing so.
An interesting thing to study would be running patterns of people born without one or both arms. See how they've adapted. See what works for them.
If someone born stubs for arms is swinging them when he runs, then perhaps it's hardwired in the brain.