10% of people are left-handed. There is some genetic basis for handedness.
My 6 year old was like that, although he now writes with his right hand. Even now, he will do the computer mouse with his left hand or throw a ball with his left hand. His grandma and great-grandma were both lefties.
You may want to help him pick a hand for writing- maybe right, only b/c I think life is a bit easier for righties. However, maybe he is more of a leftie! Supposedly if you someday have a stroke, you recover better if you are a leftie b/c of how your brain is wired.
Are there any lefties in your family?