Hand fans of various shapes existed around the world since ancient times, but if you mean the folding fans that often have batik designs, they were invented in early medieval Japan and spread throughout Southeast Asia via China
https://twitter.com/bharbhieee/status/1441041859757838338
Despite being essentially a foreign adoption, the folding fan was popular enough that it became a part of the culture in every Southeast Asian country, even reaching as far as Bengal, making it truly pan-Asian. Today they're usually only seen in classical dances 
Folding fans became popular in 17th century Europe, especially among women. I can only assume it was because of western pop culture that the fan is often mistaken as being exclusively feminine, even among westernised Asians
But in Asia, the folding fan was more commonly associated with upper-class scholars than any particular gender. You might have even seen them held by the literati in black-and-white Malay period films
In both Malaysia and Indonesia, folding fans are still used in traditional dances and martial arts
With the erasure of Malay traditions, and the compartmentalisation of culture according to racial lines, the folding fan has become a signifier of Chinese identity in Malaysia in recent decades. The generic "fan dance" is commonly used to represent the Chinese community
But even the tourism industry can't deny the folding fan's prominence in traditional Malay culture, and Southeast Asian culture in general
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