Some vegans do it because killing animals is morally bankrupt.
Some vegans do it because raising livestock is unsustainable. There is not enough land on earth for everyone to have a meat diet.
Some vegans do it because it's healthier. In general you can expect to ingest less toxins by eating lower on the food chain.
I'm not sure what vegan principles are violated by GMOs. I don't know of anyone who is actually against GMOs, the debate is around labeling them not banning them.
Personally I don't understand why someone wouldn't want to eat pesticide/herbicide drenched food. It's how we're going to feed the third world.