Here is what a professional writer, Joe Posnanski, had to say on this subject:
"Dad’s favorite ballplayer was born left-handed. Think about that for a minute: Brooks Robinson, the best who ever played the hot corner, was born with the one physical quality that should have prevented him from ever playing third base. All his life he would do everything else left-handed — he shot a rifle lefty, he played tennis and ping pong lefty, he signed autographs left-handed.
When Davey Johnson saw his hero sign an autograph left-handed, he decided to try writing left-handed too, hoping it would make him into the same sort of heavenly defender.
It did not. But how could it?