COSMOPOLITE IN A CAFÉ - O HENRY

"A Cosmopolite in a Café", takes place in a café at the evening, when it is crowded. The narrator sits at small table with two vacant chairs.Everything begins when a man,who calls himself “cosmopolite”, enters the café and takes one of the chairs. He tells that he had traveled around the world and knows all about multiple countries. But at the end the narrator concludes that the man is not a cosmopolite.

Why does he think so?