I don't unless I try really hard, and even then sometimes I can't. Sometimes only one arm swings and the other just sort of flaps loosely to my side. I still remember when I was taught (in a dance class) to do it, and they said to swing your arms "naturally", and described that as opposite to the foot going forward, and that was the first I heard of it.
When I was first diagnosed, the doctor noted my lack of armswing over and over again. Another doctor was so dead set on teaching me to do it that he'd deprive me food if I didn't.
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"In my world it's a place of patterns and feel. In my world it's a haven for what is real. It's my world, nobody can steal it, but people like me, we live in the shadows." -Donna Williams