Why is O’Brien ashamed of this story?

Are you referring to "On Rainy River"? After a long buildup, and the climactic decision in the boat, O’Brien ends the story with a paradox. The fact that he was a coward made him do the bravest thing imaginable: place himself in a life-threatening situation. The New York Times book review of O’Brien’s book was titled “Too Embarrassed Not to Kill." Embarrassment and shame turn out to be the pervasive themes of the book.