What does the 꾸 in 말대꾸 mean?

ANSWER: phrase?

My Korean-English dictionary defines 말대꾸 (-對-) as "a retort" or "a severe (incisive) reply," and the verb 말대꾸하다 means "to talk back," something parents do not like their kids to do.

Anyway, the 말 in 말대꾸 is obviously the pure Korean word for "talk," and the 대(對) is the same 대 that is used in the Sino-Korean word 대답 (對答), which means "a reply" or "an answer." So, even though 말대 (말對) and 말대답 (말對答) essentially mean the same thing, Koreans do not say 말대; instead, they say either 말대꾸하다 or 말대답하다 for "to talk back," though 말대꾸하다 seems to be used more often than 말대답하다.

So, why do Koreans say 말대꾸 instead of just 말대? Well, I think the 대꾸 in 말대꾸 was originally 대구 (對句), which literally means "a responding (對) phrase (句)" but can translate as "a rhyming couplet," like those used in poetry.

Apparently, Koreans used to play a rhyming game where one person would start a rhyming couplet and another would finish it. So, 말대꾸 (-對-) was probably originally 말대구 (말對句), which instead of having a negative connotation had a fun connotation.

Below is another story from "Eo-u's Unofficial Histories" (어우야담 於于野談), written by Joseon scholar and official Yu Mong-in (유몽인 柳夢寅), who lived from 1559 to 1623 and whose pen-name was "Eo-u" (어우 於于). The story is about a young Chae Mu-il (채무일 蔡無逸) and his doting grandfather Chae Su (채수 蔡壽). Chae Mu-il was a talented Joseon civil servant (문신 文臣), a writer (문인 文人), and a painter (화가 畵家), who lived from 1496 to 1546. His grandfather, who lived from 1449 to 1515, was apparently also talented since he held many positions in the government, including being the governor of Chungcheong Province (충청도관차사 忠淸道觀察使) and the top official at the Saheonbu (사헌부 司憲府), which was kind of like the Supreme Court of the Joseon Kingdom. Chae Su was also headmaster of Seonggyungwan (성균관 成均館), which was the top educational institution in the Joseon Kingdom.

What follows is the story of Chae Mu-il (채무일 蔡無逸) and his grandfather Chae Su (채수 蔡壽) playing a game of "responding couplet" (대구 對句). Pay attention to the number of syllables and other similarities of the couplets.
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Chae Su (蔡壽 채수) had (有 유) a grandson (孫 손) named (曰 왈) Mu-il (無逸 무일), [whose] age (年 년) [was] barely (纔 재) five (五 오) or six (六 륙) years (歲 세) [old]. Chae Su (蔡壽 채수) one night (夜 야) was hugging (抱 포) Mu-il (無逸 무일) while (而 이) lying down (臥 와) [in bed when he suggested they] first (先 선), [before going to sleep], make (作 작) a one-phrase (一句 일구) poem (詩 시). [He] said (曰 왈), "[My] grandson (孫子 손자) night after night (夜夜 야야) reads (讀 독) books (書 서)--NOT (不 불)!

[This] caused (使 사) Mu-il (無逸 무일) to reply (對) to it (之) with the response (對曰 대왈), "[My] grandfather (祖父 조부) morning after morning (朝朝 조조) [drinks] alcohol (藥酒 약주)--intensely (猛 맹)."

Chae Su (蔡 채), another time (又 우), [when] out in the snow (於雪中 어설중) [and] carrying Mu-il on his back (負無逸 무일) while (而 이) walking (行 행), made (作 작) a couplet (一句 일구), saying (曰 왈), "[Where] dogs (犬 견) run (走 주), apricot (梅 매) blossoms (花 화) fall (落 락)."

[When his grandfather] finished speaking (語卒 어졸), Mu-il (無逸 무일) replied (對曰 대왈), "[Where] chickens (鷄 계) walk (行 행), bamboo (竹 죽) shoots (葉 엽) grow (成 성)."
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Apparently, where there were dog tracks in the snow, there were also apricot blossoms on the ground, and where there were chicken tracks, there were bamboo shoots sticking up out of the snow, suggesting that chicken poop is good fertilizer for bamboo.

Notice the similarities in the rhyming couplets. This old story suggests to me that Koreans who lived centuries ago were just as clever and playful as Koreans who live today.

손자야야독서불 (孫子夜夜讀書不)
조부조조약주맹 (祖父朝朝藥酒猛)

견주매화락 (犬走梅花落)
계행죽엽성 (鷄行竹葉成)

From Dong-A's Prime Korean-English Dictionary (1998)

From 동아 새 國語辭典 (1992)