Bluth joins a cult briefly every year - it's my own fault (3,5)
I believe the answer is:
mea culpa
'my own fault' is the definition.
(Latin phrase meaning 'by my fault')
'bluth joins a cult briefly every year' is the wordplay.
'bluth' becomes 'me' (where the crossword setter is 'Bluth').
'joins' is a charade indicator (letters next to each other).
'briefly' means to remove the last letter.
'every year' becomes 'pa' (per annum).
'cult' with its last letter taken away is 'cul'.
'me'+'a'+'cul'+'pa'='MEA CULPA'
'it's' acts as a link.
(Other definitions for mea culpa that I've seen before include "I'm guilty (Latin)" , "Acknowledgement of one's guilt (Latin)" , "'I am to blame (3,5)'" , "Admission of guilt by the old Romans" , "Old Roman admission of guilt" .)