Lyric discussion by ComradeTiki 

Cover art for Fur Stop Caring lyrics by Right Away, Great Captain!

I believe "my Captain" is a metaphor for his conscience, here.

"If my Captain ever died I'd be right here directing my attempt, pursuin' absolution." Without a conscience, he would be pleading for forgiveness and showing off a religious turnaround in order to save himself.

Instead, he faces the consequences of his action like a man. "Fair to me and fair to you..."

If only his wife could recognize this bravery and acknowledge the man she is losing...

My Interpretation

It's a story of a sailor who's captain, the second "love" of his life dies in front of him. He literally means "captain". Also it's "If my Captain NEVER died". He's saying he wouldn't be in this situation if his captain hadn't died and changed him. "I am not me".