You can eat the most nutritious diet in the world and still not have optimal health, if you don't exercise. I started jogging regularly in early March after 28 years of a mostly sedentary lifestyle. Recently I've added some yoga and weightlifting also. I feel stronger, leaner, and more positive, and plan to keep regular exercise a permanent part of my life. Vegetarianism is not necessarily the optimal diet for humans.
Humans are omnivores - able to digest both plants and animals.
The main reasons so many meat-eaters are having health problems from animal products now are that the meat of domesticated animals bears little resemblance to that of the wild game our ancestors ate, and that most modern humans are far more sedentary than primitive people were. Domesticated animal flesh has more saturated fat and is often loaded with drug and pesticide residues. Even fish, which are not generally farmed, are heavily contaminated due to the poisoning of our waters. Don Wiss has a page on paleolithic diet resources with some very interesting reading, including a lengthy but very informative interview on paleolithic vs. vegetarian diets . Excess grain consumption can deplete calcium stores.