You may want to repost this one in the Argentina section which is a separate section.
In any case, the best business class to Argentina from Europe is very much a personal decision.
I prefer Iberia from Madrid, although others may find the service a little different from what they like.
Iberia have two flights per day and some days a third service is added.
You also have Lufthansa , KLM , Air France and ITA
Not sure what allows you to connect easily ex LUX.
BA is flying via Rio de Janeiro at the moment - this may go back to a direct service if volumes recover.