There was speculation back then that it was all about Khaddafi's maneuver away from the dollar. As part of that, Italy was very into pushing NATO for intervention to depose him because they were afraid he'd take his billions out of Italian banks. And then there's Benghazi....the closest port to oil fields which a western oil company was developing in western Egypt. (remember, we did the regime change thing in Egypt, too, but they took their country back).
Makes one wonder why the Benghazi situation never got to the courts, and nobody was held responsible.