My informant is a student who originally came from Korea, but moved with her family to Los Angeles since her middle school.
Bird flies away, Pear drops off.
My informant told me Korean also use this kind of four-word phrases to convey some philosophy as Chinese people do; many of them are written in Chinese characters but pronounced in Korean.
For this specific one, she said, “You didn’t do anything, but something happens coincidentally, then people think you did it.”
It is quite interesting to me that there are many metaphors like this in asian cultures, which I think more or less relates to their hieroglyphic language (especially traditional Chinese) that allows them to randomly connect two things that share similar features together.