I think the more precise word for the training soldeirs go through is "indoctrination". There's a point-by-point "brainwashing vs. incotrination" document out there, created by the Marines, that shows
why the Marines are so different from the Moonies, but for the life of me, I can't locate it right now.
The biggest thing that separates cult brainwashing from military indoctrination is that fact that you KNOW what you're getting into when you join the Armed Forces. You KNOW what point of view they have, what their goals are, what you'll (likely) need to do to succeed, and what you'll probably wind up doing during your tour of duty. Oh yes: and you also know that there'll come a time when you'll be allowed to leave.
All "extended duty tours" aside, there IS a maximum amount of time you can be held in the military: until the tour is over, or you're injured mentally and/or physically and are unable to continue.
The word brainwashing brings to mind The Manchurian Candidate: someone who is no longer able to think for themselves, was forced into the situation against their will, or at least was lied to (by omission or otherwise). Indoctrination should allow you to still think on your own, albeit with a slightly skewed point of view; brainwashing doesn't. And once you're brainwashed, you can never leave without help, or some kind of traumatic experience to snap you.
Sometimes it looks like the Army only wants dumbshit, brainwashed kids to carry rifles and shoot people, but you can't run an effective, brainwashed army. They're not inventive enough to outthink their enemies on their own: once they're cut off from their superiors, they fall like the proverbial Jericho wall. You get yelled at and screamed at in basic training to "break you down", so they can build you up into what they need you to be. And, yes, often the military is filled with idiotic, scheming, incompetant officers whose only incentive is to subjigate you and make you into their own personal slave. And this
never happens in the real world, where your corporate supervisor:
* steals your ideas to further his agenda
* lies to get a bigger budget
* drives a big car, while you're stuck with yesterday's Yugo
* berates you because you can't do anything about it if you want to keep your job and pay your rent....
And if you think the US Armed Forces have a "master-slave" relationship between officers and enlisted, you aughta take a look at some other armies, like Russia's....