Left-hand side?

[[TC]►BP◄]

It's because some people have difficulty determining what's left and what's right. By saying left or right hand side, they think of the hand they write with, or the opposite hand they right with in some situations.

Or also to make it clear that it's on the side of your hand, instead of one side of an object or person you're looking at, for example your left hand side would be their right eye if you're looking head on to each other.

And yes, I'd be very offended if I had no hand.