There are studies showing correlations between cancer, heart disease, high blood pressure, diabetes and eating meat in great quantity. Or, more accurately, there is a perceptible reduction in the risk of these problems when cutting out or reducing animal products and, crucially, replacing them with vegetables, grains, nuts, seeds, legumes, etc. While I wouldn't suggest anyone use the 'health argument' for becoming vegetarian or vegan as there isn't nearly enough peer-reviewed studies on the subject, there are demonstrable health benefits to replacing meat, especially heavily processed red meats such as sausages, with the non-animal-based alternatives. It's not fully corroborated or 100% provable, but the signs are there. More studies need to be made. I'm just pointing out that humanity would likely be healthier if we did not eat any animals products besides things like fermented drinks such as kefir (made with cows milk) or treats such as handmade cheeses and instead ate naturally occurring fruits, vegetables, nuts, seeds, grains, legumes, etc..
You can find a lot the studies done
here, if you're interested. I'll paraphrase what the registered dietitian who writes the articles says on the topic:
In my opinion, replacing meat with healthier substitutes is the thing to pay attention to. It's not that meat is inherently unhealthy; more that the alternatives are significantly healthier in almost all areas.