Culture and place are closely intertwined. People love their culture and country and are often proud to belong to their country. Without borders, how would we know where one country or culture begins and where one ends?
Borders define where one culture begins and where another ends. After living in one place for a long time, people form the societies and lands they want to live in and begin to feel belonging. A community forms, and this community's experiences are forever embedded in that shared territory. People belonging to a culture in a specific territory should decide who to include and exclude in their territory. Politically determined borders achieve that goal. Borders preserve cultural resources. Cultural representation is important to individuals and communities, which can be seen when thinking about Native American tribal lands in the U.S.  Borders are necessary to preserve cultural and historical resources and to protect such cultures from changing too rapidly from immigration.
Open borders will not destroy culture because immigration brings more cultures into contact with other cultures. Freer movement creates more diversity and expands cultures by introducing new ideas and customs. Borders do not preserve culture; people and culture create and preserve borders between cultural differences. Abolishing national or politically determined borders would not destroy culture because societies already distinguish themselves from one another by natural geography, language, or even sports teams.  Culture transcends borders. A person’s culture does not disappear when they migrate to a place with a different culture. People adapt their own cultures to new cultures. Borderlands, ambiguous spaces between politically determined borders, show how cultures can mix, form new things, and cause antagonism at the same time.
[P1] National or politically determined borders protect a country's cultural heritage. [P2] Cultural heritage is worth protecting.
Rejecting the premises
[Rejecting P1] Open borders will not destroy culture because borders do not determine where one culture ends and begins.