A pet peeve is a wonderfully visual little idiom. It is quite easy to imagine each daily encountered individual stringing their personal annoyances along behind them. Each irritation is then one's own pet; a piece of their personality and hopefully, their responsibility. While many different people may share a pet peeve, the connotation is that these peeves are uniquely annoying. A situation interacts with a specific personality to then become annoying to said person.
Peevish, which is recorded as far back as 1393 (peyvesshe), is possibly a representation of the Latin perversus, "reversed, perverse." Its current meaning is first recorded around 1530. The word peeve is a fairly recent creation, being a back formation from 1908.1
'Which is what?' you ask. This is something that happens fairly often in the English language, where most speakers are perfectly willing to make an ass out of u and me. Bad joke, I know, but the point remains that a back formation is a word that is created based solely on the assumption that an existing word must've been derived from a created word. It's rather confusing to spell out, so here's an example that I find to be amusing. At some point someone assumed that the noun burglar (the existing word) must've been derived from the verb, to burgle (the created word). Even though the assumption is false, the usage becomes so common that the word is legitimized.2
If anyone can think of a very recent back formation, please /msg me and I will add it to the writeup.
kthejoker says: An excellent modern back formation is "televise" or "televised" from television.