I like that you mention this about primates. I know a lot of vegans. I'm a vegan chef. Not a vegan... I cook for vegans....and I know very few that prattle on about the benefits of a vegan diet with any real conviction. It seems more of a supplemental argument for not wanting to hurt animals, which is the main reason I hear for people "going vegan". Which is fine of course. Until you lock a chicken in your bathroom for its own good (I'm exaggerating-i have no clue where indoors this chicken lives-maybe I missed it)Chickens are not vegans or even vegetarians.
I am not at all sure you can convince this person of anything. As my grandmother told me, you cannot argue with an idiot. Just curious. Why do you think the chicken is Cornish X and Leghorn? That doesn't make any sense to me.
If someone wants to be a vegan fine, but don't pawn off that diet on other critters. To those that go on how healthful and natural a vegan diet is, it may be of interest of them to know that not a single primate in the wild subsists on a purely vegan diet. Not one. Chimpanzees even hunt and kill other animals for food.