This is our pigeon-in-a-box, who lived with us for a day until we could get her to people who can properly reset her dislocated shoulder. Her name is Emily, just like Eloise's pet pigeon. I never realized how creepy birds' eyes are until I watched hers at close range for a while. They are OPEN. And circular. And no matter where you are, they are watching you.
I'm imagining an equally creepy anthropomorphic animal land where there's lots of inter-species dating... say there's a predator, like a cougar, who's used to dating other predators with eyes up front and a brow that makes the eyes appear more closed and oblong. Then one day she decides to broaden her horizons a little and go to a prey bar to meet some chicks. Ahem. Normally these kinds of animals aren't alive very long in her presence, and so naturally upon entering the prey bar, she would get the feeling that all eyes are on her. This is of course intensified by the natural design of the eyes of prey- they are literally watching everything, eyes wide open, all the time. This would be very startling for a predator, and probably quite uncomfortable- as would the focused gaze of a predator be to an animal of prey. I can imagine the domestic fights between them: "You're always looking all squinty-eyed at me, as if you're ready to pounce the moment I do something you don't like." "Well, I feel like I can't do anything without you knowing about it- your eyes are like searchlights the size of a crater."