The anime depicting the origin of O-ren Ishii was one of the most tragic and beautiful scenes in Kill Bill. But do we know why her parents were murdered by a Yakuza boss? It didn't make sense to me why a ganster would murder the family of a US soldier stationing in Japan.
This has never been explained, and it looks like the upcoming combined/extended "Kill Bill: The Whole Bloody Affair" also won't explain this, since the longer anime sequence seems to mostly deal with a fight between O-Ren Ishii and the "long haired killer":
What’s going on with that is originally back when Kill Bill was going to be one movie, I wrote an even longer anime sequence. So you see in the movie [O-Ren] kill her boss but then there was that long hair guy… The big sequence was her fighting that guy. I.G. [The Japanese Anime Studio] who did Ghost in the Shell said we can’t do that and finish it in time for your thing. And [plus] you can’t have a thirty-minute piece in your movie. I said okay. It was my favorite part but it was the part you could drop. So we dropped it and then later when I.G. heard we were talking about doing Kill Bill: The Whole Bloody Affair — they still had the script so without even being commissioned, they just did it and paid for it themselves. It’s really terrific. Anyway, The Weinstein Company and myself were talking about actually coming out with it sometime, not before the year is out, but within the next year with limited theatrical engagement as well.