'Argentinian' originates from the name 'Argentina' with the English adjectival suffix '-ian', where '-ian' meant 'belonging to or relating to'.

'Argentina' itself comes from Spanish 'Argentina', which was derived from Latin 'argentum' meaning 'silver'; English formed 'Argentinian' by adding '-ian' to the country name to mean someone or something from Argentina.

Initially connected to the Latin root meaning 'silver' via the place-name, over time the term came to mean specifically 'of or from the country Argentina' rather than anything about silver.