Why does Henry's father refuse to allow his son to speak Cantonese at home but require him wear to a button that reads 'I Am Chinese' whenever he is out of the house?

Henry's father likely wants his son to assimilate to American culture by speaking English at home. Requiring Henry to wear a button that identifies him as Chinese may be a way to foster a sense of pride in his heritage when he is outside the home. It's possible his father believes the button will help Henry navigate potential racism or discrimination in the community.