This is what I call the "Forks over Knives" fallacy, which erroneously equates the consumption of any animal foods at all with everything that is wrong in Western diets, without even attempting to remove the confounding factors of food processing and the quantities of the allegedly evil food being consumed.
Dr. Gregor actually admits the fundamental problem with no-meat diets, although he buries it on his site:
"There are two vitamins not available in plants: vitamins D and B12. There is a serious risk of B12 deficiency (see also here, here, here, here, here) if no supplements or B12-fortified foods are consumed, a particular danger for pregnant and breastfeeding mothers and their infants (see also here). It can lead to Vegetarian’s Myelopathy, paralysis, a variety of other problems, thickened arteries, and can shorten one’s lifespan. Two other nutrients to keep an eye on are iodine – which is harmful in too great or too small amounts (it is especially important during pregnancy, and can be found in sea vegetables), and zinc. Also recommended are yeast- or algae-based long chain omega 3 fatty acids. Rare genetic disorders may also require special supplementation." From: http://nutritionfacts.org/topics/plant-based-diets/
Then he confounding asserts that nutrients should be obtained from foods, except that you need supplements to account for ones you'll be lacking because he told you not to eat the foods that contain them. These kind of mental gymnastics make little sense unless there is another agenda besides human nutrition. Which is fine to have, but misleading to not admit it up front.
Absent his agenda, his conclusion should be the same as Michael Pollan's: "Eat real food, mostly plants and not too much" -- not "don't ever eat some of the things that contain what your body needs and take pills instead."