"Argentine" goes against the linguistic norms of nationality nomenclature, a quaint, somewhat xenophobic (and founded on racism) term like Spaniard, when it is better to use a term like Spanish, an accepted suffix that the British prefer for themselves and their home nations , but refuse to give to their historic enemies.
Countries like Canada, Australia, Austria, India, Colombia, Bolivia, and almost all other countries ending with "a" have their nationalities and national adjectives ending in "-ian", so why not the ARGENTINIANS?