"White people have no culture" Does not imply that all white people have a monolithic culture. His response misses the intent of the sentence.
The goal is to play word games so that "White people have no culture" is accepted as true, so that it can be displaced by third world culture, which will destroy all of the civilizational scaffolding that gives people that ability to use a handheld supercomputer beaming magic signals through the air to say extremely fucking stupid things to the whole world.