Why? Because it's wrong to eat meat. Neanderthals who ate meat progressed past their vegetarian counterparts because they lived a brutish and unenlightened lifestyle. With the benefit of modern technology and nutrition information, as well as a healthy sense of morality and empathy for all life, modern humanity is ready to evolve away from living through the suffering of other animals.
However, humanity is by no means populated solely by the enlightened, financially-secure, and well-educated; therefore, there are many societal pressures to continue to eat and use meat and meat products. Focus on the degree of cruelty you are promoting in your daily activities. There is a difference between the atrocities of different meat-eating activities, for example the factory farming where animals are physically, psychologically, and even genetically tortured before being sent to your plate is slightly more brutish than the "caring" butchery of Kosher butchers and Farmer Bob on his family farm. Free range only is better than eating whatever mystery meat you see; eating only fish is better than all types of meat; eating just dairy and eggs is better than all meat and meat products; wearing no leather is better than wearing all animal skin, and so on. Every little bit of caring helps. And the emotional and physical rewards you feel while living vegetarian and caring for animals will make it easier and easier to continue to live a cruelty-free life.
Lets's go over this again:
Why not eat meat?
It's bad for your health.
It's bad for the animals.
It's bad for the environment.
It's convenient to eat meat, and meat tastes good. Maybe those are more important values, but I choose health, animals, and the environment.
I find Peter Singer to be a great inspiration to remind me of my responsibilities.
because it's fully possible to live a healthy vegetarian (and even vegan) lifestyle. It's easy to get plenty of protein.