Fares
International (outside the United States/Canada and Hawaii/Puerto Rico/U.S. Virgin Islands)
For fare purposes...
an infant is defined as a passenger under 2 years of age
a child is defined as a passenger 2-11 years of age.
Availability of fares for infants and children varies depending on your travel plans. Additionally, AA.com is currently unable to book a reservation for an infant traveling internationally as a lap child. Please contact Reservations for further information assistance.[website link edited]

The answer seems to be that AA don't allow an online reservation for 'infants' (children under 2) to travel as a lap child internationally. It looks like there will be a charge and you have to call (although they strongly recommend purchasing a seat). As you've seen for yourself, they do allow free travel as a lap child on their domestic routes.

The explanation for the apparently higher fare for the child will be due to the fact that a telephone agent won't quote a cheaper web fare. I'll bet if you telephoned and asked for fares for 2 adults and a child, the child fare would be cheaper but may still be more than a web fare.