Setting aside the very strange episode on Boston Legal, in which the firm must defend a man who wants to marry a cow (the man is played by Michael McKean: would anyone else willingly play the character?) so Denise, on Shirley's behalf, closes her argument with references to Leda & the Swan and other mythological tropes...What is the fascination?
Despite myriad sheep jokes in shows like Vicar of Dibley, I suggest the trope's attraction is something more emotional than mere availability. In Eli Easton's How to Howl at the Moon, in which dogs are able to change into humans, Lance's boyfriend complains, "Why can't I have you like this and have Chance [the dog version] at the same time?"
As Aesop's fables indicate, animals embody specific characteristics, including quite lovable ones. Although humans try to compartmentalize other humans (as well as aliens: all Vulcans are logical), such humans have a nasty habit of breaking out of their proscribed boxes. And, too, traits that are popular with humans one decade become radically unpopular the next.
Animals are far more trustworthy.
In Out of the Silent Planet by C.S. Lewis, Ransom reflects on the various sentient species who reside on the planet Malacandra:
Each of them is to the other both what a man is to us and what an animal is to us. They can talk to each other, they can cooperate, they have the same ethics...But then each finds the other different, funny, attractive as an animal is attractive. Some instinct starved in us, which we try to soothe by treating irrational creatures almost as if they were rational, is really satisfied in Malacandra. They don't need pets.
Very insightful!
However, I suggest that Ransom gets close but misses the mark slightly. The attraction of animals is not merely interesting and lovable and definable differences but (1) the idea of loyalty or, at least, consistently--sure, a "pet" lion with gnaw your head off, but the lion is, in the meantime, consistent to its nature; (2) the atavistic attraction within humans to violence or contained violence.
As biological beings, we are animals, and that "id" part of us never loses its awareness of the pack or the chase. The animal becomes human while the human is drawn to the animal.
The immensely popular Who Would Win? animal-versus-animal books nearly always end with a death: real nature--not cutesy "we can appease the gods" so-called nature. There is Venn diagram overlap here between horror and fairy tales (think, Little Red Riding Hood). We want closeness to animals, including wild animals, and correctly fear that impulse at the same time.The animal spouse solves the problem.