Why is a clock considered an inappropriate gift for an elderly person in China?

ANSWER: Because in Chinese Culture, a clock is "a symbol of the end of life." That is why the grandfather in the following sentence is angry when he receives a clock as a gift. (The sentence comes from the book Schaum's Outlines: Chinese Grammar.)

我(아)送(송)給(급)爺(야)爺(야)一(일)個(개)鐘(종). 爺(야)爺(야)不(불)但(단)不(불)高(고)興(흥), 反(반)而(이)非(비)常(상)生(생)氣(기).

I 我 gave 送給 grandfather 爺椰 a 一個 clock 鐘. Grandfather 爺爺 was not only 不但 not 不 happy 高興, on the contrary 反而, [he] was extremely 非常 angry 生氣.

It reminds me of the old song "My Grandfather's Clock."
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