Was King David left-handed?

I've heard different people say that King David may have been left-handed. There's probably not any proof to back it up, but why do people say this? I've heard them say it's likely because of the strategy and everything employed in his military endeavors, which seems to come with lefties such as Julius Caesar, Napoleon, and Alexander the Great. What are some of the reasons for us to think he may have been a lefty?