Apparently the real Captain Phillips wasn't like the "hero" that we see in this motion picture. Apparently the real guy was unlikable and difficult to work with. Regardless, this is still a well-acted flick, Hollywood always changes true stories into fiction. They did it with that awful movie Dangerous Minds and if you do research on ALL the films from true events they won't be 100% accurate either.
People in the labor union he is a member of openly partied when they announced in the union magazine that he was retiring.
Of course, the pattern in every movie or tv show I have watched is that the captain is a perfect human, always makes perfect decisions, is likeable, and a hero. Often its the second in command who is made to be an idiot or just less intelligent.
The way he acted just wasnt realistic. They tried to make it real at the end when he was with the medic, but that just made the earlier scenes even more unrealistic.