That line of reasoning is that countries are only for the people born to them, so if you allow other cultures into a country it will destroy the country. It is an easy way to deflect blame for your country's problems onto an already marginalized minority.
> Countries are for the people living in them, regardless of where they were born.
If the country is composed of people who don't want to give up their culture or ethnic majority to foreign migrants, then shutting down foreign migration is completely justified. Thank you for admitting that.