I think we all have a predominant eye. I don't remember how to test for this, but I remember doing something to that effect when I started archery. I know that I have to use my left eye in the viewfinder. Whenever I try to use my right eye, I just don't feel comfortable and it doesn't feel right to me. I have no clue as to why this is, but that's the way it is for me.
Hello, fellow archer! To find your dominant eye you point your finger at some distinct object far away. Keep your finger not very far from your face (1-2 feet), do not extend your arm. Point quickly, without thinking. Now, keep your finger where you pointed it and close one eye at a time. You will notice that you point exactly at the subject with one eye (it is right in my case) and off-target with the other eye. The eye that shows you your finger at the target is your dominant eye. Repeat this test a few times to make sure you got it right.
I'd suggest to use your dominant eye to look through the viewfinder.
When I shoot my bow, I keep both eyes open. I look through the sight with my dominant (right) eye and ignore the other (left) eye. However, in photography I find it somehow difficult, so I look with my right eye and shut the left one.
Edit: Deezey sent a similar answer when I was writing mine...