This is a very good question, and I will do my best to give you some good arguements and compelling reasons.
1. It takes 2500 gallons of water to produce one pound of beef. This figure takes into account the water used to grow the cattle feed, the water directly consumed by the cattle, and the water necessary for processing the cattle into meat for our tables. In contrast, it takes only 25 gallons of water to produce one pound of wheat.
2. Many restaurants, such as McDonald's, buy most, if not all, of their beef from South American suppliers. For each pound of beef that makes it into a hamburger or steak, over 200 square feet of rain forest was destroyed. Since these massive herds of cattle graze the land to death,more and more rain forest must be cut down to provide them with food. Overgrazing by cattle strips all vegetation from the soil, which leaves the land barren. When it rains, there is nothing to hold the topsoil (the layer that is rich enough to grow grass) in place, and it washes away. Once all the topsoil is eroded, nothing will grow. And that topsoil must go somewhere, right? It does. It goes into the waterways, where it chokes out native fishes.
Even in the US, livestock farming is responsible for 85% of all topsoil erosion.
3.While cattle DO produce a lot of methane, which is one of the so called "greenhouse gasses", farmers burn a lot of fossil fuels heating and cooling the enormous structures that factory cattle are raised in. It also takes a lot of fossil fuels to produce the electricity that runs the lights 20 hours a day on egg farms (so the hens will lay mass amounts of eggs), not to mention the heating and cooling of their massive egg barns.
4. Because cattle, chickens, and pigs raised on factory farms are kept so tightly crammed together, farmers feed them over 15 million pounds of antibiotics per year, just so that they don' get sick. Herbicides, chemical fertilizers and pesticides are used in massive amounts to grow the food the animals eat, and all of these things make their way into the soil, water and air as pollution.
5. A person following a vegetarian diet needs less than 1/2 acre to produce all of his food for one year. A person who regularly eats meat needs over 2 acres of land to produce all of his food for a year.
If you need more reasons or just want to research this topic further, there are any number of good books at your local library, and scientific papers that can be found online. Please be careful when accepting a statistic as fact from any source that may be biased, though. It's easy to twist numbers into "facts" to support only one side of an arguement. Consider your source, and think with a critical mind before you make any decisions.
I hope this has helped enlighten you, and I wish you the best in trying to go "greener".