I always considered Argentina part of "the west" - it's in the western hemisphere and the common language is Spanish, along with other cultural connections to Spain. What definition are you using?
Geographically it's also dodgy. Is Australia not part of the West?
But, by your definition are not Mexico or Brazil 'the west' too? Is Argentina not more like these countries that your typical European country? Isn't there a valid distinction there?
For me - and this is a subjective but common understanding - 'the west' is all Anglo speaking countries (inc Australia and New Zealand) and western Europe (France, Germany, Spain, etc). This unit, seems to move in the same way financially, culturally, politically.