Why do only mammals react to caresses?

Mammals care for their young. The young of mammals therefore have contact often with their parent (usually the mother as males rarely provide parental care). Such contact are often necessary for physiological as well as psychological reasons. The parent's warm body provides comfort and safety. Licking not only keeps the fur in good condition, but some infant mammals actually need to be licked for them to urinate.

Even adult mammals, especially those that are gregarious or social, often groom each other, or they may sleep in close contact with each other. In nature, most animals are solitary and they do not like to be touched because being touched often means being attacked by predators or individuals defending their territory. That is why mammals are rather exceptional because they have evolve to enjoy being touched. Mammals also have evolved social bonding between parent and young. Such bonding is necessary for parental care to be given. When 2 individuals are bonded to each other, the hormone oxytocin is released when they interact socially, and oxytocin makes mammals feel good. When a mother cares for her child for example, oxytocin is released. When two lovers caress each other, oxytocin is also released. When we pet a dog or a cat, oxytocin is also released, both in us and in our pets.

There are videos on youtube of reptiles doing this. I have even seen a video of fish doing this, a Canadian man befriended an eel in the wild and every time he scubas the eel comes to him [and only him] and gets close to him so he can pet it. Also videos of sharks doing this. I have not seen videos of amphibians doing this, but then again I have not looked.

Fact is most pets are mammals, so people only generally have that experience.

Bird's do this also. E.g. watch video in link. Possibly some amphibians and reptiles too.

Probably linked to experiences learned while being nurtured when young, as it acts as a bonding mechanism.