To the average non USA person, anyone born as a US citizen is an American. Not an Irish or Norwegian or Chinese American but an American. I speak as a Moroccan, Spanish, Bulgarian, French Briton……. The English of course are Danish/German/Dutch BrIrish. I used to live not so far from the site of the last battle between the British and the English at Hingston Down in 838.
The point being that you are of the culture you grew up in not of the culture of your ancestors even if it is a valued part of your self identification. However, we digress.
More relevantly if the USA backs Argentina Western Europe sees the writing on the wall and moves to get away from becoming a political colony of a tyrannical USA. Many major token gestures but reinforces the development of the European Union into both a political and a military union capable of equipping it‘s forces from within the Union and eschews US purchasing and the removal of US forces from Europe. Possibly Canadian, Australia and New Zealand begin to fear the USA too. The Monroe Doctrine, whatever it’s original intentions, is seen in South America as implicit USA suzerainty and tHe OP action will hardly assuage that. The Chileans will be well pissed off too and look for a military backer against US support for Argentina. Does the USA want to find itself backing Argentina invading Chile?