This is just speculation, but I have doubts that Edward Kenway is actually an assassin. Don't worry, I have my reasons. This isn't just random headcanon. This is unfinished. I have so more reasons that I will add in later. I will also make changes to the points have already made. And if I'm in a good mood I'll add pictures and sources at some point, too.
Pirate and an Assassin?
Okay, I don't think I need to remind everyone of the The Creed. The first Tenet of The Creed is to "Stay your blade from the flesh of an innocent". While the word "innocent" leaves room for interpretation, and some Assassin's don't consider interogation targets to be "innocent", civilians who are unaware of the Templars or Asssassins are considered innocent by all Assassin's. An Assassin who intentionally harms civilians is no longer serving the cause of the Assassins. We know Edward is a pirate. We know that Edward is a pirate- a person who attacks civilian ships for personal gain. It seems very unlikely that these two lifestyles are compatible. Darby McDevitt has stated that Edward's primary motivation is to "get rich and prove himself a man of quality to his family".
Ubisoft's Vague Description.
Ubisoft have never described Edward as an Assassin. All we have so far is: "A pirate trained by Assassins". Edward has also been described as "conflicted". This could mean that Edward was either raised as an Assassin and eventually went on the run (much like Desmond ), or joined the Assassins and left them, possibly even getting on their bad side in the process. As far as the Assassin's involvement in the game goes, all we know is that Edward becomes "enamoured with their struggle".
Is Edward "Agnostic"?
Another one of the details released about Assassin's Creed IV, is that Edward had a major impact on the Assassin-Templar conflict. As I said, I'm not convinced Edward is an Assassin, but I doubt he's a Templar either, as Templars don't approve of slaughtering innocents either, especially not for personal gain. Ubisoft have also claimed that Edward is "one of the most uniquely conflicted heroes in the series". I am therefore led to believe that Edward is personally conflicted when it comes to the ideas of freedom and control. Very little has been mentioned about the state of the Assassins at this point, and even less about the Templars. Perhaps Edward somehow managed to temporarily unite the Assassins and Templars? William Miles said that there had been "moments" when the Assassins and Templars had worked together. Obviously we don't know what this impact is yet, but it is probably going to be one of the many inevitable plot twists in the game. Which brings me to my next point...
Ever since we discovered Clay's blood on the wall of the Abstergo lab, the storyline of the series has had enough twists and turns that I could make a seperate blog just listing them. Every game has had at least one major plot twist. In Assassin's Creed II, Minerva and Clay revealed the existance of the First Civilization. In Brotherhood, well... the ending. I don't think I need to say anything else. Revelations? Well, Ezio calling out to Desmond was even more shocking to me than when Minerva did it. And as for Assassin's Creed 3, Haytham's entire existance was one plot twist, followed by the fact that he was a Templar. I could go on, but I'd rather get back on track before I start rambling. My point is plot twists have been a major part of the series since the first game, and occured much more frequently as the series progressed. I doubt this will change with Black Flag.