what is the relationship of shame and courage ,accordi g to O'Brien

The line between courage and shame becomes blurred in the narrative. Tim felt it would have been more courageous to run to Canada rather than go to the war.

In "On the Rainy River," O'Brien tells why he, or should I say why his fictional character actually went to Vietnam. He almost went to Canada instead. His reason for going to Vietnam rather than Canada is not what you think though. What stopped him, ironically, was fear. "All those eyes on me," he writes, "and I couldn't risk the embarrassment. . . . I couldn't endure the mockery, or the disgrace, or the patriotic ridicule. . . . I was a coward. I went to the war."

Obrien considered himself a coward because he WENT to war.