The reason to switch sides and be able to shoot with both eyes has nothing to do with depth perception or peripheral vision, in my opinion. It’s simply that if you shoot with one eye closed, you see the gun in sharp focus. And the better you see it, the more likely you are to aim it—which is the worst way to shoot a shotgun. Your eye-hand coordination and subconscious mind are much more effective at putting a gun on target than your conscious, aiming mind can ever be. With two eyes, you can “see through” the gun, and it appears as more of blur, allowing you to keep all your focus on the target, where it belongs.