[1][2] Iturriaga went to elementary school in Mexico, but at the age of 13 his family returned to Europe where he attended St Edmund's College in Ware, Hertfordshire.
[2][1] In 2002, aged 18, Iturriaga joined Athletic Bilbao following in the footsteps of his brother Iñigo,[4][5] and meeting the criteria of the club's philosophy despite his birthplace by having developed as a footballer in the Basque region.
[2] Iturriaga was definitely promoted to the main squad for the 2006–07 campaign,[6][7][1] but only appeared in four La Liga games as the side finished one place above relegation (17th).
His debut came on 15 October 2006, as he came on as a substitute for Pablo Orbaiz in the 58th minute of the 3–2 away win against Gimnàstic de Tarragona;[8][2] during his spell at the San Mamés Stadium, he was mainly restricted to Copa del Rey matches.
Hugo Sánchez, the legendary striker who played in Spain for twelve years and was then in charge of the national team, stated that he would have him in consideration and follow his progress.