The first search I did when joining this site today was "Animals" because I've had a personal theory that our minds (or maybe just mine) are somehow missing some functions of the normal human brain, and therefore we can associate better with the simpler brains of the other mammals.
That is not to say we're not intelligent; in fact I think the opposite, as we probably more use the intelligence (especially logical) part of the brain due to the fact that we are not using the other functions. But some social functions of our brains are less active, as I believe they are in most other mammals. I wonder if we get along better with cats than dogs in general, as cats are less social. I get along with both, grew up with both, and have both now, but I identify better with the cats. Both cats and dogs associate well with me, and I tend to be their best friend in the household, even if they are not my pet.
Like another poster, I never have had difficulty looking into the eyes of animals, but I am extremely uncomfortable looking into the eyes of my own species. Thus, I am horrible at interviews, but excel at work.
Maybe there is something to the old saying that the eyes are the mirror to the soul, and maybe we are uncomfortable reading or letting other people read so deeply.