what anon said,they don't use eyes for emotional cues. that's why we,and some other animals,have white around the iris,so we can tell when someone is looking at us,dogs have developed the ability to pick up those cues too.
The one that won't look in the eye knows its not the dominant one.
Animals don't use the eyes for emotional cues.
i think I read on Reddit recently that dogs and humans are two of the only species that use eye-cues.
Animals have other ways to do the equivalent of the stare down. Cats stand tall and raise fur. Peacocks display their plumage. Deer show their antlers. Bears stand on their hind legs. That sort of thing.