All contemporary nationalisms are based on constructed and imagined narratives about history, geography, culture, ethnicity and religion.There are several reasons I've chosen cosmopolitanism over nationalism. For one thing, nationalism implies 'us vs. them', with a decided preference for us. It perpetuates a dualistic outlook on the world, and contrafacilitates seeing the gray areas and thinking critically about reality.
Secondly, I prefer to encounter racial, ethnic and cultural variety. The variety keeps me from becoming complacent. It challenges my thinking and helps me see a broader, more colorful world. Also, it simply is more fun.
However, I do not support an unexamined diversity. When someone claims that sexism, heterosexism, ethic superiority, or some other similarly divisive and/or oppressive attitude is integral to their culture, I would ask them to purge that attitude from their culture. To my thinking, cultures, like people, need to grow up, and shed immature attitudes, such as sexism, in order to join in on a healthy cosmopolitan discourse.
For a well-written, thoughtful and deep book on cosmopolitanism, I recommend Cosmopolitanism: Ethics in a World of Strangers by Kwame Anthony Appiah. Additionally, his The Ethics of Identity goes further into exploring living one's identity in an ethical manner in a cosmopolitan world.