The major reason that Stockdale says life is not fair is because bad things can happen to you even if you do not deserve them.
I'm not so sure that he is really proving his point, but Stockdale says that he felt life was not fair when he got shot down. He said that he had been in the top job that any Navy fighter pilot could have. So he was on top of the heap. And then he got shot down and put in the POW camp. All of a sudden he was completely powerless. To him, that showed life is not fair.