Note that the "slave galley" is one of those annoyingly persistent anachronisms that films like Ben Hur foisted upon us. The Romans didn't have those.

Navies in the ancient world, including the Roman one, were not rowed by slaves, but by paid free men. It is only in the early-modern period, during the great naval struggles between the French, Habsburg and Ottoman empires on the Mediterranean, that predominantly slave-rowed galley fleets became a thing. (And even then, traditional naval powers like Venice stuck with free rowers as long as they could, in the belief that this would result in superior performance.)

Why would they have asymmetrical development? They'd pull with both arms, no?

I've never rowed in crew, but do those rowers (eg 4/8 man boats) switch sides?