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me generation

n. A generation concerned solely with themselves.

Wikipedia
Me generation

The "Me" generation in the United States is a term referring to the baby boomer generation and the self-involved qualities that some people associated with it. The baby boomers (Americans born during the 1946 to 1964 baby boom) were dubbed the "Me" generation by writer Tom Wolfe during the 1970s; Christopher Lasch was another writer who commented on the rise of a culture of narcissism among the younger generation. The phrase caught on with the general public, at a time when "self-realization" and "self-fulfillment" were becoming cultural aspirations to which young people supposedly ascribed higher importance than social responsibility.