John Mackey, who is a vegan, told CNBC Make It that he believes meatless burgers and chicken wings may be good for the planet, but the believes they do no favors for your health. 

'If you look at the ingredients, they are super-highly processed foods,' he said. 

'I don't think eating highly processed foods is healthy. I think people thrive on eating whole foods. As for health, I will not endorse that, and that is about as big a criticism that I will do in public.'

Mackey is also the co-author of the book The Whole Foods Diet, which promotes eating a whole foods, plant-based diet for a 'long, healthy, disease-free life.'  

One of the biggest companies that offers plant-based 'meat' alternatives, Beyond Meat, sold its first products - vegan chicken strips - in Whole Foods in 2013.