When I was a wee child, I started to write with my left hand. My parents thought I was a lefty. I was actually mixed-handed, throwing and grabbing primarily with my right-hand. I wrote lefty.
My father bought me a left-handed baseball glove, which stunted my baseball development and is likely the only reason that I am not now enshrined in the Baseball Hall of Fame in Cooperstown, NY.
Make sure your child is a genuine all-around lefty.