Putonghua and Cantonese

學生：Putonghua is not Chinese.
我：Putonghua is not Chinese? What is Chinese then?
學生：Cantonese is Chinese.
我：Cantonese is Chinese. Putonghua is not Chinese. What do mainland people speak?
學生：They speak Putonghua.
我：Chinese people speak Putonghua. And Putonghua is not Chinese. So Chinese people don't speak Chinese?
學生：(thinking ...) Oh, yes! Putonghua is Chinese.