Argüello was born in León, he studied fine arts at the Royal Academy of San Fernando in Madrid, and in 1959 was awarded a Special National Prize for Painting.
Argüello lahir di kota León, Spanyol, belajar fine arts di Royal Academy of San Fernando di kota Madrid dan pada tahun 1959 dianugerahi Penghargaan Nasional Khusus untuk Melukis.