or

Random, but I've just now realised centaurs can't shake hands with the milkman.

They hold the reins.

What do humans do with their arms when they are sprinting?

In all the media I've seen the arms basically just stay in place, half bent.

If you'd imagine how much something like a centaur would need to eat, they'd probably carry snacks.

This is why they're usually carrying a weapon. Not to fight, but so they won't feel awkward with their hands.

Naruto running, all the time

"Humans can't run, what would they do with their arms?"

Got me thinking of a centaur version of "West Side Story" and snapping their fingers while performing and dancing to "Cool."

maybe you can't stop thinking about it but I'm built different

They do the Choo Choo train with their arms.

They play the accordion!!

Naruto running, but with his hands holding onto his own reins