After reading this article I reviewed several verified studies, and there does appear to be a possible link between meat and neurodegenerative diseases. This article (as well as others) argues that the culprit may be meat that is from CAFO animals (confined animal farming operations). Specifically, when animals are confined with hundreds of animals and eat a diet that may be tainted or not indigenous to the animal (ex: cows eating meat instead of plants) they could get sick and develop prions (basically infected proteins). Then they can pass on these prions to humans if we eat the meat with the prions (think mad cow disease).
The take-home message is that if you eat meat, it is probably a good idea to try to eat organic, or at least cage-free, plant-fed meats.