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.

Earlier in this section, Morrie is talking about how he believes in the inherent good of people, but admits that society is what destroys them.  He argues that humans become "mean" when they are threatened, and gives the example of how money drives our culture.  When it comes to making money and keeping it, and the possibility of losing it, he basically explains that people only look out for themselves.

The "subculture" he advises Mitch to build for himself then, is one that obeys society's basic rules, but does not allow society to deem what is important for individuals.  Essentially, he's telling Mitch to create his own values or his own set of things which are important to him.  He specifically advises him against letting what is popular among everyone else be the determining factor for what is important.  He then uses himself as an example of someone who has been able to do just that.

Here's what I mean by building your own little subculture," Morrie said. "I don't mean you disregard every rule of your community. I don't go around naked, for example. I don't run through red lights. The little things, I can obey. But the big things- how we think, what we value-those you must choose yourself. You can't let anyone-or any society-determine those for you.  (155)