Thanks all for the advice! Indeed, the security staff (are they airline staff or EZE staff) wanted to interrogate both of us for check-in, and we also did have to have the BPs before getting the dep. tax stickers. EZE has so many lines...

1. Line up for pre-check-in security questioning
2. Line up for check-in
3. Line up for dep. tax
4. Line up for security screening
5. Line up to check out from duty free if you buy something in the maze they force you to walk through.]
6. Line up for secondary security screening for liquids at gate (I assume only for US and other 3-1-1 destination countries).
7. Line up to board.