They were career military, all of them. Proven officers with real ability. But in the military you don't get trusted positions just because of your ability. You also have to attract the notice of superior officers. You have to be liked. You have to fit in with the system. You have to look like what the officers above you think that officers should look like. You have to think in ways that they are comfortable with.
The result was that you ended up with a command structure that was top-heavy with guys who looked good in uniform and talked right and did well enough not to embarrass themselves, while the really good ones quietly did all the serious work and bailed out their superiors and got blamed for errors they had advised against until they eventually got out.
That was the military. These teachers were all the kind of people who thrived in that environment. And they were selecting their favorite students based on precisely that same screwed-up sense of priorities.