Eaton is a lefty. Lefties can't play 2B because they will have a hard time setting up the throw to 1B for a double play.
More than a hard time, he'd have to be a contortionist. I cannot think of a left handed major league second baseman in the past 100 years.
(For that matter, I cannot think of a left handed shortstop, third baseman, or catcher, although they don't have the same issues. You'll find left handed shortstops, third basemen, and even catchers, in high school. You won't find second basemen. Well someone here probably has seen one, I haven't.)