Story spoilers ahead! [spoiler]AC4 showed where Haytham came from, from pirate Kenway. He learned how to fight from his father obviously, but he never grew up with the assassins to learn their values. The order is too frayed while the templars are organized and always plotting. Just look at the modern state of the assassins (in game terms of course lol), they're just a rogue group doing espionage while the templars are psuedo corporations with hidden motives. It only makes sense that the Assassins are frayed and losing purpose, it's the reason why the templars are so powerful in the modern age.[/spoiler]