What is the paradox in chapter 4 of The Things They Carried?

In The Things They Carried, Chapter 4, The Rainy River, the paradox is between bravery and cowardice.

The narrator, Tim (O'Brien), tells a story about how he was an anti-war activist. He was then drafted. He was shocked and frustrated, and waffled between running away to Canada to avoid the draft and simply going. He does not want to disgrace his family, but neither does he want to go to war.

He says, "I survived, but it's not a happy ending. I was a coward. I went to war" (244).

The paradox here is that he went to war, which is an act of bravery but he called it an act of cowardice.

He considered it to be cowardly because he wimped out of leaving the country and sidestepping the draft. He chose to conform and go to war so his family isn't ashamed.

That should about do it, right ?