It's absolutely not easy. For example, there is still no conclusive evidence on meat causing cancer. There is no mechanism - there are no carcinogens in meat. What was actually found was that processed meats, and also meat cooked on open fire or otherwise charred may contain carcinogens. Still nothing on meat prepared in other ways, i.e. boiled.
To provide at least somewhat credible proof, it would be required to find groups of people, who do not eat read meat at all ever, then other group - who eat read meat but not processed or cooked on open fire, and finally a group that only eats processed or cooked on open fire meat. And even if you could identify such groups of people, how could you possibly eliminate all other potential confounders?
Same with vegetarians vs meat eaters. Vegetarians on average are more health conscious: more exercise, less smoking and alcohol, more healthy habits in general. It is completely wrong and dishonest to just compare them to meat eaters and say "see, how many benefits you get from not eating meat".
But are all the effects of not eating animal products at all in the long-term well known?
Again, it is not very easy. Groups of people who avoid animal products on the grounds of i.e. religion (Buddhism) do not stand out as remarcably healthy. And groups of people who are vegetarians for health reasons have many healthy habits that confound meat avoidance as the reason for their better health. So no, it's not quite conclusive as well.
I've recently read "The Blue Zones" book. The authors identified areas where the unexpectedly high percentage of centenarians live, and did some research to try and find out the possible reasons behind their longevity. The interesting thing is that people consume at least some meat in all of these zones, except for about 30% of Loma Linda's Seven Day Adventists, who are vegetarians.
So there you go: even if meat is not a hard and fast requirement for health and longevity, it certainly is not a source of sickness and shortened lifespan.
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