That’s why Argentina needed to be Pro Axis…
From a strictly historical point of view: Argentina’s government at that time (a Military dictatorship) had pro-German bias. That was specifically about cultural/institutional reasons since most Argentine Army officers had received training from Prussian military institutions.
However, the economic ruling elite (rich cattle & grains producer landowners) were strongly pro-British. And that was because of both cultural but above all economic reasons: Argentina was a huge exporter of cattle&grains to the United Kingdom (that the UK especially needed during war time), and a buyer for UK’s industrial goods.
Most of the people (not that anyone cared) had pro-allied feelings.
So, even if the governing Military Dictatorship had a taste for fascism, Argentine economy (and the economic well being of the landowners whose economic interest the Military were defending) relied on trade with the Great Britain.
All that resulted in an odd situation where the Military Government liked Germany… but Argentine foreign policy was leading to maintain neutrality… and maintaining neutrality was the best option for, well, for the United Kingdom! That was because as long as Argentine were neutral German U-Boats couldn’t torpedo Argentine cargo-ships carrying grains to the UK.
Too sum up: Argentina’s neutrality was a de facto support of Great Britain’s war time economy.
A different matter was the relationship with the USA. The Americans wanted all South American countries to declare war against the Axis powers. That idea was resisted by both the Argentine Military Goverment (both because of their pro-fascist ideology and because of the economic interest of the landowning elite), and by London (because of the reasons explained above).
The Argentine Military Government’s fascist ideology would have taken as far as allowing the German pocket-battleship Graff-Spee to seek safe heaven Buenos Aires’ port (if she had managed to scape from Montevideo and reach the Argentine Capital)… but it’s un-clear how much help the Argentine government would have given to the German ship after all – breaking with the UK would have been like killing the Golden Laying Eggs Chicken for the Argentine economy.
So from an historical point of view anything but a stric neutral Argentina doesn’t makes sence.