One argument is practical: meat production is an inefficient use of the world's resources and can be more damaging to the environment. From PETA:
"U.N. scientists have determined that raising animals for food generates more greenhouse-gas emissions than all the cars, SUVs, trucks, and planes in the world combined. Researchers at the University of Chicago determined that switching to a vegan diet is more effective in countering global warming than switching from a standard car to a Toyota Prius."
It makes sense from a logical point of view too: instead of producing plants for human consumption, we produce plants to feed to animals for human consumption. But I'm not an expert on the environmental impact of meat production, so I'll move on to the second argument.
The second argument is ideological. If you eat animals, you are operating on the assumption that animals exist to serve the needs or desires of humans. From this point of view, nature exists primarily for human use. I suspect many environmentalists balk at the assumption that nature exists not for itself but for human use. Indeed, common arguments in favor of environmental causes involve the preservation of animal species: we fight global warming in part to save the penguins, to save the polar bears. But if you eat meat, whom are you really trying to save the environment for? Not for the animals, whom you believe may die for your pleasure. Eating meat contains the explicit assumption that the needs and desires of animals don't matter, and the implicit assumption that nature exists for humans to use in any way we see fit.