I don't know about the Argentinian site, but I live in Brazil & the Brazilian site is an absolute nightmare!

If you don't have a CPF (Brazilian tax number), you can't book through there easily.

The ONLY way I know to do that is to register for a Multiplus account (Latam's FF account in Brazil) & login. When you book (as long as you book far enough in advance), you'll get an option that says "I just want to make a reservation" (Eu só quero fazer uma reserva). Once you've done that, call Latam using your local number & pay over the phone with your credit card.