To be honest I don't know if a lot of vegans would like to even argue that the diet is healthier. Most vegans I've met would argue that its morally important to eat vegan even if its less healthy than eating meat. YMMV though.
This is an important comment. Vegans would tell you that veganism isn’t a diet, it’s a lifestyle choice. I’ve been vegan for over 10 years and it’s never been about health for me, it’s been about not exploiting animals.
Another angle on your and GP's comment is environmental. The most environmentally friendly meats come from the most mistreated animals, particularly broiler chickens in warehouses, but most veg*ns aren't going to say, well, if you absolutely have to eat meat, you should eat those.