Franco, are you asking why do we have pets?
I think from a more simplistic viewpoint, us humans enjoy "taking care" of things. It's another way for us to feel needed. Also we usually receive a positive response (appreciation) from our pets by doing so which is our reward. It's a social thing too. Many people refer to their pets as "kids".
My dog needs her food dish filled and she's always happy to see me when I come home..
Great answer, and you point out it can even involve several dimensions of our emotional behaviour and that much of it is reciprocal on the part of the pet, a feeling of kinship. And kinship there certainly is.
The Science Daily article attempts to explain the origins and why it was beneficial to the survival of early man, things that formed our emotional and behavioral makeup. The study of our kin, the animals can throw a lot of light into the black hole of human behaviour.
The last words of King Arthur were, according to Tennyson in his " Passing of Arthur," " The whole round earth is bound by gold chains about the feet of God". Finding the nature of those chains is incumbent to our survival.