I have an MFA, and I enjoyed almost every single second of getting one. Yes, even living on $600 a month and teaching freshman comp. I loved that. Beans and rice was, and is, my favorite meal.
That said: an MFA ain't worth the paper it's printed on. (And it's not much paper, either: of my high school, college, and MFA degrees, I think the MFA is the smallest, like 4 by 5 inches, as it should be. The high school one is the largest, and God knows I earned that one.)
When I was an undergraduate, my teachers told me, "Whatever you do, do NOT go into debt for an MFA!" More sage advice has never been given. All you potential people who might want an MFA: do not go into debt. It's not worth it. Only get one if they pay you to go.
If anyone really claims that the possession of such a silly degree means that a person is in some way a better writer than anyone else, well, they're lying, deluded, or working for a university with a brand new MFA program. All an MFA means is that someone in a writing program somewhere liked your submission enough to let you in, and that you cranked out enough stuff to stay in. That's all.
Most writers show up at writing programs already knowing how to write. That's how they got in. And once they get there, they're totally resistant to being taught anything. Ask most writing teachers and they'll tell you that undergraduates are MUCH more fun to teach, because they're open to learning a thing or two and trying new stuff. Not so true with the graduate students.
So why are they there? Many reasons, but "learning to write" is rarely up there. They want the two years of concentrated writing time (a dream come true for me, really), they want to reorient their lives toward writing, they want the teaching experience so they can become college teachers one day.
But CAN you learn to write in an MFA program, if you want to? Of course! You can also learn to write in a community college, or by reading Orwell during breaks from your job at the tomato-packing plant, or just by writing a shit-load and giving it to your best friend to read. There are as many different ways of becoming a writer as you can think of. All are legitimate. No one is born knowing how to write.
If a writer with an MFA has an easier time getting published than one without, it has little to do with the degree or the school and EVERYTHING to do with the people she or he meets there. Editors and agents are much more open to reading stuff that comes with a personal recommendation. They don't, and can't, give every submission the full, impartial attention it might deserve. This sucks. It really, really does. If I were to change ONE thing about publishing, I would wave my wand and allow agents and editors to see every single piece of writing with a fresh, energetic and unbiased eye.
That said, the "connections" that one might get with an MFA are usually not much more than a name and an address. The connections are a way to get out of the slush pile. But there are lots of ways to get out of the slush pile. Going to conferences is another way. Entering contests, publishing in small mags, and meeting other writers are all other ways that are every bit as effective. Sleeping with a published writer works really well!! Take it from me!!
Also, and maybe this doesn't need to be said, but I don't think you have to be from a privileged background in any way to get into an MFA program. No one on the admissions committee cares if you went to Fredonia Central High or if you went to Miss Emily's Country Day. All they are about is if they like your stuff. And that's a complete and total crap shoot.