For a long time, I thought the old legend said "strong carps can become dragons." But I knew this was not true. The legend in China didn't say all carps can become dragons.
It was the Book of the Later Han (5th Century) which says "the carp who finished swimming against the stream at "Dragon Gate" Yellow River, became a dragon."
This means carps in Japan or in the United States cannot become a dragon, no matter how strong it may be. It has to be at the dragon-gate, Yellow River in China.
This legend eventually produced a belief and custom of Koinobori in Japan, the strong carp swimming upstream can be a good luck for a successful growing. It also produced a famous idiom of the "Upstream Dragon Gate （登竜門）" which means "a gate to dragon", "a gateway to success" or "the important step for a successful career."