I've never had to fly internationally with an infant, but this does sound familiar. I think its a pretty standard rule. I did look up the fare rules for a first class ticket DFW-EZE and both American and the generic IATA rules list this condition.
Writing a nasty letter won't get you anywhere, for sure. That is definitely a lot money for an infant but it is clearly spelled out in the fare rules. You could redeem another First award.
Originally Posted by American Airlines
Children Discounts
FROM/TO ARGENTINA NOTE - GENERAL RULE DOES NOT APPLY 1ST THROUGH 4TH ACCOMPANIED CHILD 2-11 - CHARGE 75 PERCENT OF THE FARE. TICKETING CODE - BASE FARE CODE PLUS CH OR - 5TH AND EACH ADDITIONAL ACCOMPANIED CHILD 2-11 - NO DISCOUNT OR - INFANT UNDER 2 WITH A SEAT - CHARGE 75 PERCENT OF THE FARE. TICKETING CODE - BASE FARE CODE PLUS CH OR - INFANT UNDER 2 WITHOUT A SEAT - CHARGE 10 PERCENT OF THE FARE. TICKETING CODE - BASE FARE CODE PLUS IN OR - UNACCOMPANIED CHILD 2-11 - NO DISCOUNT.
Originally Posted by Generic IATA Fare Rules
Children Discounts
UNLESS OTHERWISE SPECIFIED NOTE - GENERAL RULE DOES NOT APPLY ACCOMPANIED CHILD 2-11 - CHARGE 75 PERCENT OF THE FARE. TICKET DESIGNATOR - CH AND PERCENT OF DISCOUNT OR - INFANT UNDER 2 WITH A SEAT - CHARGE 75 PERCENT OF THE FARE. TICKET DESIGNATOR - CH AND PERCENT OF DISCOUNT. NOTE - UNACCOMPANIED INFANT - NOT PERMITTED OR - UNACCOMPANIED CHILD 2-11 - CHARGE 100 PERCENT OF THE FARE OR - 1ST INFANT UNDER 2 WITHOUT A SEAT - CHARGE 10 PERCENT OF THE FARE. TICKET DESIGNATOR - IN AND PERCENT OF DISCOUNT. NOTE - UNACCOMPANIED INFANT - NOT PERMITTED