I tried to research this a while ago, and I think the numbers work out to say that going from a "standard" American omnivorous diet to a "standard" American vegetarian diet corresponds to a CO2 emissions reduction equivalent a one-way NY-SF flight or drive. Going from that to the a vegan diet is about equivalent to avoiding the return flight or drive.
So if you've already avoided having children, and already avoid flying and driving, then going vegan is probably one of the best things you can personally do to reduce your CO2 emissions. But if you haven't yet done those things, changing your diet, while a step in the right direction, may not be enough to effect a major reduction in your emissions.
(Sorry for lack of references --- I'll add them up if I can find them again. They were surprisingly hard to find the first time. Corrections appreciated if I've misremembered the figures.)
For instance having a couple of hens in your backyard may be exploitative in your book, but it provides a rich, free source of food (several hundred eggs every year), while consuming all of your food remains, vegetables peels, rotten fruits etc. in the most efficient way imaginable. And the hens would be perfectly happy and not harmed in any way, as long as they have reasonable space with some grass and a bush to peck around.
I'd simply say that I think that we need to reorganize our world at a simpler scale, build smaller communities, sharing more local resources (like backyards and chickens and potato plots), step back on globalisation, reduce our consumption and environmental footprint, reduce division of labour, share work more, ...
Save the world by eating bacon!
Anyway, I sometimes think it's quite funny how my own lifestyle is so much more green than the average "green" person. I don't have children, I don't own or drive a car, I only use public transporation, 99% of which runs on electricity. I'm vegan, I haven't been on an airplane for like maybe 4 or 5 years. I live in a modern, energy efficient and small apartment. I buy "100% renewable electricity" in a new, energy efficient "smart city neighbourhood". And of course I recycle.
Yet I haven't really tried to be more green, these circumstances have just happened naturally.