Purely anecdotal accounts of the My Grand-Mother Ate 40 Pounds of Bacon Every Day of Her Life And She Lived To Be 120! variety do not in any way constitute legitimate evidence for the claim that meat-eating is healthy. Even less do such claims (assuming that they are true) imply that veganism is unhealthy. And even less still can they hope to undermine the philosophical justification for veganism. In any conversation about the effects of diet on human health, what must be taken into account is the broader range of controlled scientific study and statistical analysis. Considered within those contexts, the evidence very clearly suggests that a whole foods, plant-based diet is quite conducive to optimal human health and that eating animals and the products derived from them is associated with an increased risk of heart disease, cancer, diabetes, obesity, high blood pressure, and many other bodily ailments.

[Editor's note: In the two excerpts that follow, the term “vegetarian” is used to refer to an entirely plant-based diet, which is to say, a vegan diet. In strict usage, the terms “vegan” and “vegetarian” have two quite distinct meanings, but historically, the term “vegetarian” has been (and continues to be) employed by many to connote a diet that excludes all products derived from animals. In the contemporary vernacular, however, a vegan diet excludes all products derived from animals, whereas a vegetarian diet excludes meat, but permits the consumption of dairy, eggs, and honey.]

In an article entitled "Vegetarian Diets: What Are The Advantages?" published in Forum of Nutrition in 2005, Dr. Claus Leitzmann wrote,

A growing body of scientific evidence indicates that wholesome vegetarian diets offer distinct advantages compared to diets containing meat and other foods of animal origin. The benefits arise from lower intakes of saturated fat, cholesterol and animal protein as well as higher intakes of complex carbohydrates, dietary fiber, magnesium, folic acid, vitamin C and E, carotenoids and other phytochemicals. ... In most cases, vegetarian diets are beneficial in the prevention and treatment of certain diseases, such as cardiovascular disease, hypertension, diabetes, cancer, osteoporosis, renal disease and dementia, as well as diverticular disease, gallstones and rheumatoid arthritis.

In 2010, the tree-hugging lefties over at the United States Department of Agriculture published the following statement in Dietary Guidelines for Americans:

In prospective studies of adults, compared to non-vegetarian eating patterns, vegetarian-style eating patterns have been associated with improved health outcomes – lower levels of obesity, a reduced risk of cardiovascular disease, and lower total mortality. Several clinical trials have documented that vegetarian eating patterns lower blood pressure.

On average, vegetarians consume a lower proportion of calories from fat (in particular, saturated fatty acids), fewer overall calories; and more fiber, potassium, and vitamin C than do non-vegetarians. In general, vegetarians have a lower body mass index. These characteristics and other lifestyle factors associated with a vegetarian diet may contribute to the positive health outcomes that have been identified among vegetarians.

The health benefits of a vegan diet having been sufficiently, or at least credibly, established, let's return to exposing the fallaciousness of the original argument. As mentioned above, within the realm of scientific inquiry, personal anecdotes are not tantamount to evidence for the truth or falsehood of a proposition. Statistically, not all people who smoke cigarettes will develop lung cancer, but that does not mean that smoking cigarettes does not cause lung cancer. What is relevant in extrapolating the relationship between cigarette smoking and lung cancer is the percentage of smokers among those who do develop lung cancer. This percentage is known to be quite high, which (all other things being equal) indicates a correlation between the the habit of smoking and the development of cancer. This correlation has been established in numerous peer-reviewed studies around the world.

The fact that a certain, and even significant, percentage of people who smoke cigarettes do not develop lung cancer does not indicate that smoking is (to use a slightly awkward construction) not unhealthy. Nor should the fact that some non-smokers also develop lung cancer lead anyone to conclude that not smoking cigarettes does not decrease the likelihood of developing cancer. What's important are statistical averages derived from the analysis of legitimate experimental data, and not the outcomes of isolated cases.

Likewise with eating animals. A person may be able to eat animals and animal by-products and not succumb to heart disease, colon cancer, high blood pressure, Type 2 diabetes, and a host of other ailments associated with the consumption of meat, eggs, and dairy. But such a case does not undermine the numerous peer-reviewed, multi-year, epidemiological studies that indicate a correlation between eating meat, eggs, and dairy and the development of the “diseases of affluence”.

Your argument is invalid.