Last October, a member of the Aspies for Freedom web forum began a thread called "Post One Pet Hate Every Day." Other members began posting entries such as "Ignorant people," "one-button mouses," and "humans." Two weeks later, a member who hadn't contributed finally chimed in:

I avoided this thread for awhile because I thought it would be about hating until I realized it was about pet peeves.

A few years earlier, in a forum for conspiracy theory enthusiasts, someone else asked fellow members, "What is your number 1 pet hate?" After "Elites secretly controlling the world" and "People who guarantee they know the truth and refuse to think they could indeed be wrong," there came this response: 

Are we talking like Pet, as in Animal pets, hate?
If so, I hate that my dog chews everything and wants to kill small animals.
If we are talking about Pet Peeve "hate" then … I hate people who don't care about what's going on around them

Both posters had to translate pet hate into pet peeve before they could get the intended meaning.

Sometimes this is taken to be a distinction between British English and American English. For example, a commenter on an online golf forum vented his "pet hate," and got the response, "Pet hate? In the US, we call it pet peeve." In its definition for the adjective pet, the Longman Dictionary Online has a single entry for pet hate and pet peeve, specifically labeling the former British English and the latter American. The truth, though, is a bit more complicated.

Let's start with the etymology of peeve itself. The Oxford English Dictionary has peeve the noun deriving from peeve the verb sometime around 1909, and peeve the verb arising via backformation from the adjective peevish, sometime near 1900. As for peevish, the OED speculates that it might ultimately derive from the Latin perversus, though there are gaps in the story.

It didn't take long for ordinary peeves to become pet peeves. Also according to the OED, the noun pet came from the Scottish Gaelic peata, meaning a tame animal. Its adjectival meaning of "cherished" or "favorite" is attested from 1819, in a quotation from Samuel Taylor Coleridge in a letter. The ironic extension of this meaning to encompass things that are especially disliked has its own subentry.

As for the difference between American and British English when it comes to pet peeves and pet hates, the new search tools on the Google Ngram Viewer allows us to run a comparison:

Looking at the blue and yellow lines, we can see that Americans do use pet peeve a lot more than they use pet hate. Looking at the green and red lines, we can also confirm that British speakers use pet hate more than they use pet peeve—but not by that much; it's about a 3-to-2 ratio. Furthermore, until the 1940s, pet hate was almost as popular as pet peeve in American English. There was even a song copyrighted in 1934 with the title "Pet Hate."

It also turns out that the earliest attestations so far for both pet peeve and pet hate are from American English. The OED has pet peeve from 1919, in a definition in a book of jargon: "Pet peeve, the thing that provokes you the most." That fact alone tells us that the origin goes back further, and Google Books yields a couple of slightly earlier examples, both from 1917, both from American publications.

One comes in the April issue of The Illinois Chemist, a publication of the University of Illinois's chemistry department. A margin-filling joke (like the kind you can still find in Reader's Digest) at the bottom of page 24 says, "Our pet peeve: 'Yes, and he talked about the paraffin series, methane, ethane, and profane.'" Get it? Propane? Profane? Those organic chemistry newbies are too much!

The other one comes from the September issue of Illustrated World, in an article by one Ray Goldman, explaining to prospective car buyers that a car costing less than $500 might not be such a bargain, because some conveniences you might think come standard don't—such as a speedometer and shock absorbers. Page three of the article states:

Now we come to the pet peeve of the small car owner. Very frequently when the machine has stopped because of traffic conditions and the policemen on guard, the car becomes stalled because it lacks a flexible motor. This compels the driver to step out and crank up the machine on a crowded thoroughfare, and you may be sure he doesn't like to do this any oftener than he has to.

The OED's first citation for pet hate comes in 1939, from the Baltimore Sun. This is about twenty years after the appearance of pet peeve, but again Google Books pushes the date further back. In fact, it takes it back to before the earliest attestation of pet peeve, all the way to 1902, again from an American publication. The novel Life of a Woman, by Richard Voorhees Risley, describes the elderly Miss Walsingham like this:

 She had a huge sense of whimsicality and "intellectual fools," as she called them, were a pet hate of hers.

There's still more to the story. In addition to its citations for pet peeve and pet hate, the OED also has this 1880 quotation from Mark Twain's Tramp Abroad:

For years my pet aversion had been the cuckoo clock.

Once more, Google Books has an even earlier attestation, and this time it's from British English; specifically, the story "The Two Dolls" in Mary Russell Mitford's Our Village, published in parts between 1824 and 1832. The story concerns a little girl named Fanny Elvington, who had a "foolish and wicked prejudice":

But her favourite fear, her pet aversion, was a negro; especially a little black footboy who lived next door, and whom she never saw without shrinking and shuddering and turning pale.

Luckily, she sees the error of her ways by the end of the story.

Putting pet aversion into the Ngram mix with pet peeve and pet hate results in a surprising picture

The peak for the red pet aversion line is more than twice as high as the 1945 peak for pet peeve, and almost twice as high as the current reading for pet peeve. It's only around 1950 that the frequency of pet peeve and pet hate combined approaches that of pet aversion, which by then has been in decline for more than twenty years.

And in while we're in the pursuit of bigger pictures, what did people call pet peeves, hates, and aversions before pet gained its ironic meaning? They called them bête noires and bugbears. Putting bête noire into the Ngram mix… 

… it looks like they still do. Bugbear, it turns out, leaves all these synonyms in the dust, flattening the peaks for bête noire and every kind of pet dislike:

And finally, to close with the ultimate in closely nursed things that make your skin crawl, it turns out that there are even pet bête noires and pet bugbears!