Respond positively! It's great that you're child cares not only about animals but also about his diet, especially at such a young age. Red meat isn't the best thing for you to begin with, and as long as he's still eating plenty of fruits and veggies, there are still lots of other vegetarian options that will provide him with the protein he needs (and won't be getting from meat) to help him grow and be healthy. Great sources of protein are beans and legumes (such as lentils), yogurt, cheese, nuts (peanut butter is great!), tofu and grains including bread and pasta. Be happy that your son has taken an interest in the food he eats! You'll help him build a foundation of good habits and conscious eating for years to come.

Thanks for your response.
We don't eat much red meat- our family eats a very healthy diet with lots of fish and chicken and veggie dishes (including all the foods you mentioned). My son said that he doesn't want to eat any animals at all, which would limit his diet a lot. I want to make sure he eats enough protein (he's a skinny guy) and I'd rather not have to make a separate meal for him. I was a little taken aback by his comment, and while I respect his feelings I'd prefer that he eats a varied diet.

It is possible to have a varied diet without eating meat, fish or eggs. He can still eat potatos, rice, nuts, pasta, vegetables, fruit, drink milk - if he refuses coe or goat milk buy him soya or rice milk, you can buy diary free yoghurts, cheese and chocolate, he can eat lots of things just check it says suitable for vegeterians and also buy a cook book of vegeterian recepies - make him what your having but a veggie alternative. For example if dinner is chicken curry, in a smaller pot make your son vegetable and lentil curry, sand you can all eat rice, or if your having lasanga make him vegetable lasanga with no meat or use veggie mince such as quorn (made from soya as a meat subsitute) tastes like the real thing so you and the rest of the family will be happy and he will be happy that he is not eating animals. Or a roast dinner cook the potatos and veg seperately from the meat and you can all indulge!
Experiment and have fun - good luck.

Couple of points here.  First, "limiting" his food choices should not be a worry.  If he feels pressured (read-singled out) then he may react by self-limiting further.  He may not, I don't know your son.  Also, when I was 12 years old, I decided to stop eating meat.  I occasionally would eat it, if there was no alternative, but I still do not like to eat animals.  There are many different levels of non-meat diets.  There are many options for proteins and carbs regardless of his choices.  If he is doing this to avoid hurting animals, then he should understand that eggs and honey are absolutely not harmful.  Bee keepers make sure to keep more space than is necessary for the bees so that they produce enough honey to sell. Besides, he is six.  This could be a phase, or he could just need time to grow out of it.  Lastly, try google.  Maybe you can find something that will help.  Plus, and this is for your ears only, a lot of the meat industry is really atrocious.  Organic IS best.