When Morrie talks about building a person's own subculture, he means that each individual should decide what matters to them in life. It's important to obey the laws of society—he doesn't, he says, run red lights—but we get to choose what lifts us up, what shames us, and what we value.
Morrie explains that there is nothing inherently shaming about the things he's forced to go through with his illness. One example he gives is not being able to clean himself. He can choose to not be shamed. In the same way, society teaches women to value thinness and men to value money. Each society, he explains to Mitch Albom, has its own standards and problems. An individual can work to create his own subculture that takes the good parts of the culture he lives in and rejects the negative ones.
Living around other people who value the same positive things can help a person become the best version of themselves. Shortsightedness, Morrie says, is the biggest defect humans have. It's important to create a subculture that looks forward and works together to achieve their goals.