Preserving languages preserves cultural identities
Local languages represent their speakers' cultural and ethnic identities. The death of a language means the death of a valuable cultural identity.
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There is a sense of loss and sadness when the last speaker of an endangered language dies. Language means more to people than just a means of communication—it is a bridge to a cultural heritage that may stretch back thousands of years, as was the case when Boa Sr, the last native speaker of the Bo language spoken on the Andaman Islands, died in 2010. With her death, linguists mourned the loss of a person, as well as the loss of a culture.
Languages contain a wealth of cultural knowledge. Languages have unique oral histories, performance art, and ways of communicating. They also contain unique figures of speech, inspiring idioms, and amusing vocabulary. Languages are aesthetically valuable, and direct translations between languages always lose the essence of the originating language's meaning. Endangered languages should be preserved, so people can access and enjoy their language. Speakers of endangered languages work to revive their language for many reasons, including cultural connection. For example, members of the Cherokee tribe in the Eastern Band worked together to create a language immersion school for children where classes, including science and math, are taught in Cherokee. By the 1960s, the Miami language spoken by the Miami Tribe in the U.S. Midwest was extinct, but thanks to work by Miami speakers, the language is taught at Miami University in Ohio. Members of such people groups with an endangered language want to know their cultural heritage, so they take great lengths to revive the language.
People's languages are important, but content in languages can still be translated to majority languages. Languages do not shape worldview or cultural identity; people shape cultural identity. Language preservation is not necessary for cultural preservation because though a language may die with the last speaker, a culture can still live on through other documentation. In addition, people groups may choose to have their cultural connection die out in favor of a new cultural affiliation. Their choice should be respected. 
[P1] Languages contain unique cultural information. [P2] All cultural identities are valuable.
Rejecting the premises
[Rejecting P2] Just because all cultural identities are valuable does not mean they need to be preserved forever.