Question

Why does the narrator think the Spanish word tener exito is ironic

Answer 1

Because the narrator wants the reader to search what the word means and it means "to be successful" at something!!

i just gave you the answer for what the spanish word "tener exito" means, its underlined, in bold and italics!!!

Answer 2

The direct translation of this idiom is tener - to have and exito - which means success. So this translates ‘to have success’. In English we usually say ‘to be successfull’ rather than ‘to have’ or ‘to own success’.