(Excuse the title, I can never resist a bad pun.)
In many religions the right hand is considered to be sacred, or clean, and the left to be evil and dirty. Hands are also symbols of good, such as balance and praise. The things we consider to be precious we hold in both hands to keep safe.
I was recently directed to read this article. The implications are fascinating, but also it made me think about how everyone gesticulates when they talk. Without even thinking we emphasise, describe and imagine with our hands. It's such a natural instinct, it made me wonder whether it is the primary language... How did cavemen communicate before it was generally accepted that the sound "rock" meant 'rock'? I imagine they did it with their hands. And big sticks.
There has always seemed to me to be something rawer, purer and emotionally charged in sign language that rarely exists in spoken communication. Try telling someone "I like socks" without words. You have to invest far more emotion - and effort - into what you are trying to communicate to them, than if you could just say it without thought.
The words we speak we throw away, but the words in our hands have remained precious and kept safe.