Not a military member or veteran myself, but am friendly with quite a few present and former officers. The culture they describe sounds
extremely political. Almost like being a career military officer is equivalent to being a career politician. To some extent, there's a hint of academy politics as well: people who publish, get cited, etc., move more quickly than people who don't. To another extent, there's classic politics: people who schmooze within the Beltway, know how to play the media game, etc., get ahead quicker than others.
In many respects, David Petraeus is the perfect embodiment of these political principles. He published, he politicked, he maximized his media exposure, and he hobnobbed within the right DC circles. I'm not qualified to judge whether or not he was as good a leader as many believe him to have been. But he was certainly a top-notch political operative.
(Other government agencies, e.g., the CIA, have very similar internal political incentives. The game is almost the same. This may explain, in part, the fluidity between military leadership and Agency leadership).