It's obviously not my specialty, but I the history of the canine is something of a hobby of mine, so until someone else comes in and corrects me, I'm going to report some of my findings:

Animal Domestication and Human Culture

Humans domesticated animals because those animals provided certain uses to humans, and those uses informed the way humans perceived and understood those creatures.

Allow me to provide a few examples before discussing the dog at length.

The Horse. Horses, as CGP Grey calls them are "civilization game changers." Horses are the literal difference between a Kingdom that can only be maintained on foot versus the world-spanning message system maintained by the Mongol messengers, or (we can expand it to the Camel) the Camel paths through the desert that formed the basis of the Arabic empires and caliphates.

The Horse, because of its use as a military and communications machine, became extremely valuable. In mythological understanding, the horse is always a symbol of power. In culture, it is almost always associated with nobility. The Yijing constantly references the horse as a being of the Earth (as opposed to the Dragon of the Heavens) and as the avatar-esque representation of earthly power. In perhaps one of the most famous examples, the Mongols held an extremely high place for the horse and its symbol of nobility. So much so that it caused a deadly break between Temujin (the future Chingghis Khaan) and his blood brother Jamukha. Temujin, the son of "commoners" wanted to share the herds of animals equally with Jamukha, whereas Jamukha, the son of nobility, insisted that he would take all of the horses, and Temujin would take all of the sheep and goats. Sheep and goats are valuable animals: they provide wool, milk, and meat. But they are the "common" animals fit for peasants. Horses are the backbone of power and represent the noble and royal blood. This ideological break was the first split in a war that would result in fratricide and the rise of Temujin Khaan on the path to Chingghis Khaan (the difference from King Temujin to King of the World).

By the time we get to George Orwell's Animal Farm, however, far far removed from the Yijing's esoteric ramblings about symbolic creatures, and Eurasian military history, and well past the age when the horse was a creature that made and broke empires (published in 1945, after Operation Barbarossa which was possibly the largest invasion using horses, often forgotten since the tanks were more prominent in our historical imagination, and instead persist in the imagination as the foolish Polish cavalry that broke harmlessly against the Nazi tanks, a historical myth), the horses of Orwell's story are Boxer, Mollie, and Clover. Mollie is a foolish mare, so obsessed by the trinkets that the humans bestow upon her that she betrays the farm and escapes to another run by humans for the sake of sugar cubes. Boxer is a prominent character whose primary feature is his maxim "I will work harder!" and as a Napoleon loyalist (spoiler alert) and finally his death, being betrayed on his deathbed by the pigs who call the knacker instead of the ambulance. And finally, Clover, who is a companion to Boxer, and can catch the schemes of the pigs, but isn't sure what to do about them.

The horse has dramatically fallen from a position of power in the human cultural consciousness because its use peaked in the First World War and has been cornered into a place of either luxury (as in many mystery novels or series that take place in the western US) or fantasy (there's a lot to be said about GRR Martin's portrayal of the horses in Westeros vs. those in the Dothraki culture).

As a counter example, take the cow. Cows are, like the sheep and goat, commoner's animals, but are symbols of great wealth. There is some connection with the horse in that they are historically symbols of earthly power, but in societies without more abstract conceptions of money (i.e. hard or soft currency) the cow has often been used as that wealth. Partly because of its intrinsic value: cows provide milk, fertilizer, hide, and ultimately beef. A wealthy herder could provide cheese and cream, could use his bulls for breeding, could use his cows for growing larger fields, and in religious or cultural celebrations, provide a valuable and wealthy meal for his family or his village.

Probably the most disgusting representation of the value of beef I can think of is in a Korean story regarding a sick mother and a son who is told by a doctor that he should feed his mother beef. The son is poor and can't afford beef, so he decides to start slicing off pieces of his thigh to give to his mother. I can't think of any medicine that beef would provide (maybe his mother had a severe case of anemia and needed the iron?) but what it's really saying is that the son needed to provide something valuable to his mother, and being unable to do so, the son provided something even more valuable by providing a literal piece of himself.

Cow sacrifice, contrary to popular opinion, has been a staple of Vedic religion prior to the Middle Ages. Jha outlines in Myth of the Holy Cow how the Vedas, Upanishads, and Hindu mythological heroes all sacrifice and consume beef (and at times horse meat). This makes perfect sense considering that the early Aryans (the Indo-Europeans) were horse-based nomadic societies like the Mongols and Tibetans, and that horse meat and beef among these societies isn't particularly strange or unusual. Why would the Indo-Europeans be any different? Moreseo, it was only in the Middle Ages when perspectives started to change, and the Islamic Invasions of India pushed a trend towards the sacralization of the cow. Hindu temples started building cattle sanctuaries, and strict taboos were placed on cows. A sort of cult was built around cows (specifically female cows) as they are described as "mothers" and take on personifications of the earth. Why are cows sacred? Well they provide for us. Their dung is used for fire and fertilizer. We cleanse our spirit and fill our stomachs with it. Their milk is a symbol of the divine transformation (in a famous theological debate, a King asks a Yogi who God is. The yogi pulls up a bunch of grasses and says, "What color is milk?" The King says, "White." "Where does the color of the milk come from?" "From inside the cow." "But does the cow consume anything that is white?" The King looks at the grasses and says, "No." The yogin then explains that God is who works through the cow to change the color of its intake to white milk).

Today, the cow is often portrayed as a dumb farm animal. Its literal value having decayed through global economics in the same way that technology has decayed the value and human consciousness of the horse. The Irish epic The Tain literally means The Raid and specifically refers to a cattle raid of one tribe against the other. Why? Because cattle were the most advanced currency they had at the time the epic was conceived.

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