The shortest, easiest answer is that there was already a large group of German speakers living in Argentina: between 1885 and the First World war there were more than 100,000 German-speaking immigrants in Argentina. (this included German Jews and Volga Germans from Russia).

By 1945, there were millions of German-speakers in Argentina.

There had been much military cooperation between Prussia and Argentina as well... so even as late as 1945, there was a sense among military-types that Argentina was "familiar".

Finally, Juan Peron's political star was rising in Argentina--he negotiate to negotiate an arms deal with Germany in 1943--and Peron was thought (correctly) to be sympathetic to former Nazis. Peron became president in 1946.