Suppose you decide to leave the United States and live in another country. Do they have to let you stay?
You can freely leave the United States with no intention of returning, but your country of refuge has to agree to let you stay. Edward Snowden, famous NSA spy, had to have permission to stay in Russia. He also had to get permission to leave China, where he was a "tourist," and enter Russia.
Where does this "right" to enter the United States originate?