"Winners need no rationalizations!" Kaido is saying that more to himself than to Luffy. He does not truly believe that.
Like many One Piece villains, he is a fully established pirate who lost the idealism from his youth to the hardships of the Grand Line. But, if Crocodile and Moria have grown bitter by the trauma from the losses they've experienced, Kaido is hunted by his "wins".
Even if he is unquestionably strong, he does not believe that or, to be exact, he does not believe that he is worthy of his own strength or the status he has conquered. All his most important challenges have not been fully conquered by his own effort or merit: His victories were given to him by third party interference and, therefore, no matter how powerful he is, he can never truly know if he had what it takes to conquer this world by himself. Trying to hide his own shame he repeats again and again that "winners need no rationalizations" or "pirates always betray their allies".
Even if "there's no such thing as playing dirty in a battle between pirates", both Luffy and Kaido know that their victories are only their own if they did it by themselves. In the past, Kaido believed that he was the only one that could change the world and, although he has reached the top of the pirate's hierarchy, he doesn't feel like he has accomplished anything at all. While he drowns himself in sorrow and in alcohol, he sees the "losers" being praised and admired. Even his own daughter looks up to his old rival and 20 years after his most shameful victory, the World's Government seems to believe Luffy is a bigger threat than him: his own worst enemy doubts his relevance.
I can not stop to think how amazing his flashback will be...
