Firstly, I question how much Pentagonese comes from the Pentagon. Other than referring to itself as "The Building", it seems that the preponderance of the offending terms are actually military terms that migrate to the Pentagon from the field. I couldn't be sure of that (wouldn't that be an interesting study), but I can navigate the Pentagon language-wise because I know the lingo. And I've never served a day there - I learned it in the field. I suggest that Pentagonese is military jargon come home to roost because, while certainly the head of the U.S. military, the Pentagon is hardly the heart of the nation's warrior class. I couldn't imagine a cavalry lieutenant colonel fresh out of G-3/5/7 just waiting to try out his new cool-kid words on his new cav squadron. Soldiers, unlike civilians, don't usually think anything cool comes out of the Pentagon. The Pentagon is where things go to die.
No, I don't think most of that language comes from the Pentagon, I think it comes from the operational forces. And I think that's a good thing. Every technically challenging trade has its own jargon; doctors, lawyers, electricians, plumbers, mechanics, business types: they all have their own jargon that other probably think is just plain weird. But it's part of their culture, it helps each member of that culture identify others like them, it gives them a simple thing to bond over. The military is no different, except it might be exacerbated more because of the physical concentrations of military posts and combat zones. In small towns throughout the world, the local military facility is probably the biggest thing around and is therefore the dominant culture. Cultural attributes, such as language, thrive in such settings. Combat zones probably compound the use of vernacular - troops from units who would never have otherwise met each other - are exposed to new jargon and it spreads like wildfire.
It gives me a sense of belonging when I can talk to another tanker and talk about the John Wayne Pass, bitch plates, turret rides, or FMs; or talk to Iraq vets about gimlers (GMLRS), MIRC, the 3ID bridge, or Ambush Alley. To say nothing of the many "verbed" and other mangled terms that U.S. Army loves so, so much (kinetic, non-concur, transition, etc) and the even more dear alphabet soup of acronyms. These terms are expressions of our common experiences and hardships. They are things we shared and we (almost) always understand each other - it isn't important that outsiders do understand it.
Which I think gets to my final points here. Firstly, the one reason I imagine people hate this lingo is because they are on the outside and it seems foreign to them. Learn it or don't - it doesn't much matter to me. To give these types some perspective, I don't come to your place of business and bitch that I can't understand your acronyms or colloquialisms. Because they are yours. Secondly, when military types do talk to outsiders, they should stow the vernacular. It's just plain rude to speak that way and certainly not helpful if you're trying to explain to others what it is you are doing. Translate it into the common tongue, please. Thirdly, and finally, I think the biggest problem with Pentagonese isn't that you hear a different language - people would forgive a uniformed person with it. It's hearing the civilians in The Building mimicking the uniforms that is unnerving, as they are peripheral, if important, members of military culture. But it still sounds unseemly and probably why the Pentagon gets blamed for the military's torturing of the English language. All of this is to say, mock it if you will (even I do sometimes), but don't forget it's inherent to military culture. And there's nothing wrong with that.