I guess the first part of this depends on what you are asking. The phrase "brother's keeper" alludes to the Biblical story of Cain and Abel. After Cain killed Abel, God asked him where Abel was. He told God he didn't know and asked if he was his brother's keeper. When we use this phrase ("am I my brother's keeper?") we refer to the idea that we are not responsible for anyone but ourselves.
Stockdale is saying this is not an acceptable way to think in the POW camp. He says that the Americans need to stick together and support one another or else they will all fall apart mentally.