I often cook veggie food, it's delicious done right. I love curries for that; I recently did a curry night and put on something like 11 dishes; I think 7 of them were veggie or vegan. Even made my own paneer because it's not something we can buy in Andorra.
I also once had a "chilli and movie" night for some friends, one of which is a vegetarian and the others most definitely not. I made two big pots of chilli, one vegan and the other regular. The carnivores were really tucking in to the vegan one. That said, I'm not naive enough to think I can convert people to vegetarianism or veganism through proving that the food can be equally delicious as meat-based meals. I can't even convince myself of that, after all.
I know very little about the environmental benefits ( and, to be completely honest, don't have a huge amount of interest, which is probably awful, but the free time I have isn't going to be spent reading up on it, sorry

) but the few claims I've seen seem to have holes in them. They usually compare an omnivorous diet with one that is vegan AND locally-produced. When I cook veggie or vegan food, I don't specifically look for local in-season produce. OK, where I am, I don't have much choice because that's all we can get unless we want frozen, but I'm pretty sure that most people doing their shopping in Tesco are going to buy what's available rather than what is local, because, let's face it, very little is local. People are too used to being able to buy their ingredients whatever the season and I think the average person, especially one who has already restricted their diet substantially by cutting out anything that is animal-derived, is going to be seriously put off by limiting that even more drastically by only being able to choose locally-produced ingredients.
The other thing that strikes me when they talk about getting rid of the massive farms which apparently have a huge environmental impact is, OK, but what about the farmers, the employees, the land-owners, the transport companies, the people who depend on this to survive? What are they all going to find to do instead? It sounds like an economic disaster. And what about the animals; are we going to let those sub-species become extinct? Keep them in zoos? They're not equipped to live in the wild, for the most part.
And what about fertilisers for all those vegetables? At the moment, bone meal is used extensively, as it is a by-product of the animal industry. The best alternative is chemical fertiliser.
Like I said, I don't know enough about the argument, but it's pretty clear it's not black and white.