Eye contact and animals
Eye contact with humans can be a threat and a reward, depending on how it is used with animals.
With cats, if you stare directly at them and they are unfamiliar with you, they may stare back with wide-open eyes. This can be a threat response. The cat is getting ready for you to attack or is getting ready to attack you.
If you want to tell the cat that you are friendly, then slowly blink at them and turn your head away and then turn back and slowly blink a few more times This tells the cat that you want to be friends and are not a threat to them and don't want to hurt them.
If a cat is rolled over on its back and staring at you, this position says they are ready to use all of its weapons to scratch you and bite and don't want to be touched.
Dogs also use a direct fixed stare as a threat gesture.
When people see a little dog barking at them, they stare back, watching it to ensure that the dog does not bite them. Most little dogs only do this behaviour out of fear and insecurity.
Suppose you want them to know you are not a threat. In that case, you will turn your head and body away or look down to the ground and hunch down to appear smaller. Avoid directly looking at the dog's eyes - look just in front of the dog or next to it. This says you are not a threat and don't want to fight.
Eye contact with someone a dog loves can also be rewarding. If your dog barks at you while bouncing around a toy and lowers its chest but keeps there bottom in the air, they ask you to come and play.
If you turn to look at the dog, you will reward the behaviour because you have provided attention. This will reinforce the barking behaviour in the dog, and it may do it more and more. Even if you say, you don't like it.