Argüello was born in Córdoba in 1956 as the first of four children by Jorge Marcelo Argüello Varela and Raquel Luque Colombres.
In 2003, Argüello was again elected to the Chamber of Deputies and he became Chairman of the Foreign Relations Committee, and in that capacity organized the office of the Parliamentary Monitor for the Falkland Islands (Observatorio Parliamentario Cuestión Islas Malvinas).