You haven't demonstrated that my logic is faulty, first, simply by saying so.
Second, scientists have indicated that consuming flesh is a more efficient means of acquiring certain nutrients (especially protein). Meat and animal products (eggs, dairy) only comprise about 20 to 25% of my diet.
I eat mostly vegetables, legumes, beans, nuts. The fact that I also consume flesh and animal by-products does not render my diet inefficient. Medical professionals have repeatedly indicated to me that the diet I now follow is optimal for my health and survival. Since I seem to be quite healthy, I will trust the doctors on that one.
Third, we now grow sufficient food to feed 12 billion people, while the world population is only 7 billion (article does mention the inefficiency of grain-fed cattle/beef production, but does not denigrate pasture-fed animals or other means of producing meat). The cause of hunger and poverty is not a lack of food production, but rather greed and the funneling of resources into the hands of a few (also, the above article indicates that much grain is "wasted" in the production of alcohol. Thankfully, there is no such indication of wasted grapes. Wine! ). Much food goes to waste.
I compare veganism to religion, because the rationale most vegans seem to have is often based on "spiritual" notion of equality of species. I value other species, but I am human, and value other humans above other species, because they are my own species. Is that any more logical? Not necessarily so, but certainly no less. This doesn't mean I would condone the annihilation of other species, however, I have no problem with the exploitation of other species for our own survival or nutrition.
After all, plants are another species, too. We consume living things, one way or another. Plants feed on the decomposed remains of animals. Some plants trap and consume live animals (mostly insects). If it's okay to grow and eat plants, why not animals? The only answer anyone can give me are based on "spiritual" or religious concepts (that turkey in my sandwich could be my late Aunt Harriet), or simply that animals are also sentient beings. So what? They're tasty and nutritious sentient beings.
You can further diversify your low-carb, vegetarian diet with eggs and cheese, but yogurt, milk and soy milk tend to contain sugar, which increases their carbohydrate content...(emphasis mine)
A low-carb, vegetarian diet tends to provide less protein and more heart-healthy unsaturated fat than a typical meat-based, low-carbohydrate diet. This, however, is not always true. A low-carb diet based around eggs and cheese will be higher in artery-clogging saturated fat than one based around seafood and skinless chicken breast.
The measure of efficiency I'm using entails the amount of vegetable matter and the expanse of land required to feed the animals you eat. That's horrendously inefficient.
Second, your claims about protein are simply absurd. Protein can be readily acquired via soy, amaranth, and quinoa.
It is indeed true that we must eat something. But the difference is that animals have complex neurological systems--brains. They manifestly fear being led into slaughterhouses. They sense that something horrible is happening to the animals ahead of them. They know.
And I'd also point out that your distinction would be offensive to many indigenous people, including, I rather strongly suspect, several present here in this network.