I'd be thrilled to have a 'complete lack of ignorance'!
With that said I think both a completely vegan diet and an extremely low carb diet are both unhealthy for most people.
I think eating fresh fruits and vegetables (organic if you can afford them) is wonderful and eating them cooked or raw (depending on the fruit or vegetable) is very healthy and these should make up a large portion of people's diet. I also think that eggs, lean meats, and poultry are healthy and that it's ok to drink/eat some dairy as long as you're not lactose intolerant.
I tried to go on a vegetarian diet more than once, primarily because I saw vegetarians as 'thin and healthy'. When people said they were vegetarian they always looked that way. However it just didn't work for me. At first I felt so much better, had so much energy, felt less sluggish, etc. but this was just a temporary thing. I couldn't do it long term. I started feeling really yucky and worn out and the only thing that helped that was meat. So I had to go back to eating moderate amounts of meat.