DD9 is fairly ambidextrous, she writes equally well with either hand, does gymnastics as a lefty, throws with either, but for art she is definitely a righty. She takes great pride in being able to do things with both hands.
I (her mom) am a lefty, as was my grandfather and a few cousins. I would agree jack's mom - being a lefty is harder - even today, everything is made for a right handed person, from the computer mouse to the pour spouts on measuring cups and bottles to the edge of a steak knife.
I have bought various things through the years that have been made for lefties, and sometimes they work well but other times they don't.
I think if you are going to ask a kid to choose a hand, let them decide which "feels right", not one that will necessarily make their lives seem easier, because if they are more left-handed than right but are told to pick right, they may develop more issues based on that mistake.
