I told J., after a discussion of the differences between "complaining" and "criticizing", that I was going to look up the etymology of "complain." That turned out to be even more fascinating than I'd expected.
Remembering the French verb complaindre, I assumed that our English word had come from that, and that complaindre had a Latin root. That was right; the word came into English in the late 14th century, from the Old French verb (12th c) meaning "to lament" which did come from the Latin complangere, which meant "to beat the breast." I was confused by the "com" in this word; the dictionary I consulted said in this case it's used here less in the sense of "with" or "together" than as an intensive prefix. The Latin verb plangere means "to strike or beat the breast," and "plaga", a noun from this word, means a stroke or wound and is probably the origin of "plague." And of course, in a less specific sense than the-plague-as-illness, the things that plague us are those we tend to complain about...the first recorded uses of "plague" meaning "bother or annoy" date from the 1590s.
I was familiar with the word "complaint" being used to mean "lament" from its common occurrence in Renaissance church music - during penitential seasons we sing many motets with texts like, "O Lord, hear the voice of my complaint," which doesn't mean "I'm upset about all the things that are wrong in my life," but rather, "I lament my sins and weaknesses."
That sense of the word lasted only until the 17th century, giving way to the modern meaning of the word. Its popularity in the language (and human behavior) seems particularly evident in the long and colorful list of synonyms and related expressions:
moan, whine, kvetch, beef, bellyache, chide, yammer, carp, grouse, rail, crab, quarrel, nag, gripe, bespeak, bitch, and kick.
Not surprisingly, some of these also have very interesting origins as synonyms for "complain." To look at just a few of them, I've heard some of my British friends use the word "whinge," unfamiliar to me, which is related to "whine." Whine/whinge come from the Old English hwinan which is the whizzing or whistling sound that arrows make through the air. hwinsian is the whining of dogs, thought to have come from the Old Norse hvina "to whiz," and German wiehern "to neigh". The use of "whine" meaning "to complain feebly" began in the 16th century.
To "beef" about something was a slang term that originated in the 1880s. The origin is uncertain, but it's thought that it might come from a common complaint by U.S. soldiers in the late 19th century about the quantity or quality of beef rations.
"Grouse" is British army slang from the same period, first mentioned by Rudyard Kipling, and did not have to do with the lack of game birds in the military diet! Etymologists think it might have come the word "groucer", in the Norman French dialect, which came from the Old French groucier "to murmur, grumble."
And while we're in the animal kingdom, "carp" has nothing to do with the fish; the word was already used to mean "complain" in the early 13th century and probably came from the Old Norse karpa "to brag," influenced by the Latin carpere "to slander, revile," lit. "to pluck" (carpe diem="sieze the day") Together, these words somehow mutated toward a meaning closer to "find fault with."
As for "crab" in its use as a noun meaning a sour person, or a verb meaning to complain, it was probably a combination of the temperament of the animal "crab" (from Germanic roots for scratch, claw; the first mention of the constellation known as the Crab appears in English around 1000 A.D.) and the sourness of the fruit (a Scandinavian word for wild apple trees, crabbe, 13th century). The use of the word to refer to a complaining, sour person dates from the 1570s.
All of which is way more than I expected to learn when I offered to look up "complain"!