Americans are immigrating to other countries, they just like to call themselves X-Pats® because they think immigrant is a dirty word

I’m going to be a pedant and say they are emigrating to other countries.

E.g. Fewer people are immigrating to the US as it speed runs fascism. Many Americans, however, are emigrating to other countries.

Emigrate is to leave ones country for another, immigrate is to come to a country to live.

Yes that exactly how those 2 words work, they are emigrating from the USA and immigrating to other countries, but they will get offended by that