From your comments, I am guessing that you will be a hardened skeptic. You've come to the right place.
Let me address a couple of points. First, I agree with you that correlation is not causation. But my guess is that you are not looking for causation (for example, the biochemical processes that causes a higher incidence of heart disease in meat eaters). After all, who knows what causes heart disease? There are experts who might guess, but I don't think any researcher has come up with a single, definitive cause.
(EDIT start: heightening the contrast between correlation and causation.) Let's turn our attention to the causation / correlation contrast for a different health-related matter: Smoking (perhaps unhealthy) verses Non-Smoking (perhaps healthier).
Here is a proposition, turned into a parallel of the vegan/healthier argument. Does non-smoking cause not-lung-cancer? OR is non-smoking correlated to not-lung-cancer? (I apologize for the Aristotelian flip here, but just think "absence of lung cancer" as a parallel to "healthier.)
To ask for causation is to ask too much. Some non-smokers get lung cancer. See http://carcin.oxfordjournals.org/content/24/5/875.short. Therefore, there is no causal link between not-smoking and absence of lung cancer.
In contrast, science has asserted that smoking is correlated with an increased incidence of lung cancer. Now that is a different question. Even a skeptic would say there is a correlation. Non-smoking correlates to lower lung-cancer incidence.
It would be scientific, but unethical, to cage humans and force one group to smoke and not have another group smoke. It would be scientific, but unethical, to cage humans and force-feed one group meat and force-feed another group vegetables. (EDIT ends.)
A scientifically accepted way to test humans is to do an epidemiological study. One type of epidemiological study would be to monitor many people over a long period of time.
It turns out that protein intake has been studied for both monozygotic (identical) twins and vegetarianism for an epidemiological survey of a homogeneous group.
The first study is called “Dietary protein and blood pressure in monozygotic twins” by
Richard J. Havlik M.D, et. al, published in Preventive Medicine (Vol 19, Issue 1, pp. 31-35). It shows that
Using differences in monozygotic
twins, a direct association of dietary
protein intake and diastolic blood
pressure was identified and persisted
after adjustment for known covariates
of blood pressure. Adjusting for known
covariates and holding total calories
constant, a 9-g difference in daily
protein intake was directly associated
with a 1 mm Hg difference in diastolic
blood pressure.
Simply put, what they found was that after adjusting for differences other than genetics (because monozygotic twins have the identical genetic makeup), more protein correlates to higher blood pressure.
As you have noted, vegetarian diets tend to be poorer in protein. You might object that this study shows a relationship between protein and BP, not meat and BP. All that an inveterate skeptic would conclude is that this study shows a link between vegetarian diets and lower BP, but perhaps not a strong link. On to the second study.
The epidemiological study may be found in Am J Clin Nutr September 1988 vol. 48 no. 3 739-748, which you may read in full, online. It compares a large number (n=27,529) of Seventh-Day Adventists. The Adventists are prohibited from using tobacco, alcohol, and pork. They are discouraged from consuming other meats, fish and eggs. Because eating a vegetarian diet is optional, this made for an ideal epidemiological study in that the meat-eaters and the vegetarians have similar life styles and all live in the same US state (California).
Before I discuss the study’s conclusions, let me observe that it addresses almost all of your objections. It is a large study. It draws scientific conclusions, based on well known statistical methods. It minimizes lifestyle differences and geographic differences of the participants. It was published in a peer-reviewed journal. (The reviewers are, in a sense, skeptics-for-hire. Their job is to ferret out any design flaws, incorrect inferences, and confounding factors.)
The conclusion is:
Within this population, meat
consumption was positively associated
with mortality because of all causes
of death combined (in males), coronary
heart disease (in males and females),
and diabetes (in males). Egg
consumption was positively associated
with mortality because of all causes
combined (in females), and cancers of
the colon (in males and females
combined) and ovary. Milk consumption
was positively associated only with
prostate cancer mortality, and cheese
consumption did not have a clear
relationship with any cause of death.
“Positively associated with” means more x correlates with more y. (x = meat, eggs, milk; y=death for all causes, death by colon cancer, death by heart disease). If you delve into the article, you will see that the tests are very statistically significant. For the case of all-cause mortality in males, the significance (p < .0001) means that only in 1 case out of 1000 would you find that the results were due to chance.
This significance is much higher than that you would see for drug trials, for instance.
The author, Dr. Snowdon, has done his job of showing correlation. (Remember, the standard is to show correlation to a given significance, not to show causation.) He even has a section about the limitations of the study. (There were three: 1) Gathering a lot of data means a simpler survey; 2) Dietary habits may have changed since the study began; 3) He did not study what substituted for meat (e.g., fruits and vegetables substituted for meat may be the cause for lower mortality).)
His only grant was from the US National Cancer Institute, so the paper was not sponsored by PETA or the Dairy industry, for example.
If you compare the scientific studies of smoking correlating with lung cancer (for example, http://cancerres.aacrjournals.org/content/54/22/5801.short), you will see that for some studies, the statistical significance levels are still very high (P = 0.001), but not as high as the Adventist study. The relationship between eating meat and these major diseases is more strongly linked.