Old English gat "she-goat," from Proto-Germanic *gaito (source also of Old Saxon get, Old Norse geit, Danish gjed, Middle Dutch gheet, Dutch geit, Old High German geiz, German Geiß, Gothic gaits "goat"), from PIE *ghaid-o- "young goat," also forming words for "to play" (source also of Latin hædus "kid").
They are sprightly, capricious, and wanton, and their strong odor (technically called hircine) is proverbial. [Century Dictionary]
The word for "male goat" in Old English was bucca or gatbucca (see buck (n.)) until late 1300s shift to he-goat, she-goat (Nanny goat is 18c., billy goat 19c.). Meaning "licentious man" is attested from 1670s (hence goat-milker, name of a bird formerly believed to suck the milk from goats at night, but also old slang for "a prostitute," also "the female pudendum"). To get (someone's) goat is by 1908, American English, the source of many fanciful explanation stories; perhaps from French prendre sa chèvre "take one's source of milk," or more likely it is "to steal a goat mascot" from a racehorse, warship, fire company, military unit, etc.
... to become separated from your goat is a thing no soldierman is willing to contemplate. ["Letitia, Nursery Corps, U.S.A.," in American Magazine, vol. lxiv, June 1907]
"fit of peevishness, offense or ill-humor at feeling slighted," 1580s, in phrase take the pet "take offense." Perhaps from pet (n.1) on a similar notion to that in American English that gets my goat (for which see goat), but the underlying notion is obscure, and the form of the original expression makes this doubtful. Perhaps from the notion of "characteristic of an indulged or spoiled child," but OED notes that this word seems to have been originally a southern English term, while pet (n.1) was northern and Scottish. Perhaps influenced by unrelated petulant.
1530, "goat sent into the wilderness on the Day of Atonement as a symbolic bearer of the sins of the people," coined by Tyndale from scape, a shortening of escape (see scape (v.)) + goat; the whole word translating Latin caper emissarius, itself a translation in Vulgate of Hebrew 'azazel (Leviticus xvi.8, 10, 26), which was read as 'ez ozel "goat that departs," but which others hold to be the proper name of a devil or demon in Jewish mythology (sometimes identified with Canaanite deity Aziz).
Jerome's reading was followed by Martin Luther (der ledige Bock), Symmachus (tragos aperkhomenos), and others (compare French bouc émissaire), but the question of who, or what (or even where) is meant by 'azazel is a vexed one. The Revised Version (1884) simply restores Azazel. But the old translation has its modern defenders:
Azazel is an active participle or participial noun, derived ultimately from azal (connected with the Arabic word azala, and meaning removed), but immediately from the reduplicate form of that verb, azazal. The reduplication of the consonants of the root in Hebrew and Arabic gives the force of repetition, so that while azal means removed, azalzal means removed by a repetition of acts. Azalzel or azazel, therefore, means one who removes by a series of acts. ... The interpretation is founded on sound etymological grounds, it suits the context wherever the word occurs, it is consistent with the remaining ceremonial of the Day of Atonement, and it accords with the otherwise known religious beliefs and symbolical practices of the Israelites. [Rev. F. Meyrick, "Leviticus," London, 1882]
The transferred meaning "one who is blamed or punished for the mistakes or sins of others" is recorded by 1824; the verb is attested by 1884. Related: Scapegoated; scapegoating.
For the formation, compare scapegrace (which is perhaps modeled on this word), also scape-gallows "one who deserves hanging," scapethrift "spendthrift" (mid-15c.).
zodiac sign represented as a goat, or half-goat half-fish, late Old English, from Latin Capricornus, literally "horned like a goat," from caper (genitive capri) "goat" (see cab) + cornu "horn" (from PIE root *ker- (1) "horn; head"). A loan-translation of Greek Aigokherōs, the name of the constellation. Extended 1894 to persons born under the sign.