Well, our brains are asymmetrical in terms of function, and our bodies are asymmetrical internally too (heart, liver). So, which came first? Are we mostly right handed because of left brain functionality (each side of brain controls opposite side of body), or is handedness innate in some other way and perhaps influences brain sidedness? Or, are these two things unrelated?
With so many poisonous plants reptiles and insects, it is better to use the hand further away from the heart. In case it gets stinged or bitten or pricked the poison will affect a slightly more remote area.
If the subtext is not apparent: https://en.m.wikipedia.org/wiki/Just-so_story