There is a word called "Furareru" which means to be turned down for a date or to be turned down for a marriage proposal. For example, "I confessed that I like ______-san, but she coldly rejected me." The word "Furareru" generally means that things move repetitively from side to side, back and forth, but why did "Furareru" become a word that means refusal?
In Japan, a kimono is worn by women, but did you know that unmarried and married women wear different kimonos? Unmarried people wear kimonos with long sleeves, while married people wear kimonos with short sleeves. So you can tell if a woman is unmarried or married just by looking at her kimono. A kimono with long sleeves is called a Furisode.
Now let's go back to "being rejected." When a man approaches an unmarried woman, if she is interested, she would wave the sleeves of her long kimono from side to side. If the woman was not interested, she would wave her kimono sleeves back and forth. So, the word "rejected" comes from the action of waving sleeves back and forth.
Incidentally, unmarried people still wear long-sleeved kimonos, but I don't think the custom of replying by waving one's sleeves is still in existence. Also, it looks like there was no custom of men waving to women in Japan.
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