You can be left or right dominant, or neutral  a.k.a central. Dominance can shift during your life, or even during a round of Sporting Clays, it can be affected by many things like fatigue, stress, even blood sugar levels.
If you think about a shotgun it does not have sights like a pistol or rifle. This is because you do not aim a shotgun, rather you point it.
BUT you have to know where to point it. So the analogy is that the eye is the back sight and the rib is the front sight. (Forget ‘lining up the sights’ after you read this, don't do it, and don't ever look at the barrel)
If the dominant eye is NOT over the barrel, the brain is paying attention to the wrong eye and you will not be able to point the shotgun in the correct place to break the clay. You will not lead correctly and two identical targets (same distance and speed) will appear to have different leads depending on which side they come from.
In my opinion, when you are a beginner and have no history to eradicate, learning to shoot the shotgun from the dominant eye side is the best way to go. You will find it awkward whichever side you shoot from, the left is going to be better because of the dominance.
There are four or five methods of dealing with eye dominance, not everyone can cope with them. I am amazed how many people cannot close one eye for example. Your instructor will go over the methods with you I am sure, but I really recommend going lefty for shotgun.