Quite the opposite, actually. Eating meat is highly unsustainable. The United Nations has been urging us for years to move towards a plant-based diet because “lesser consumption of animal products is necessary to save the world from the worst impacts of climate change”. This is because animal agriculture is responsible for more greenhouse gas emissions, about 18%, than all the transport systems combined in the world, around 13%. It is also the leading cause of species extinction, ocean dead zones and several other environmental degradation indicators.
In fact, we could feed more people with less land, water and resource usage if everyone was vegan than if people ate meat. A Cornell University article states that the US alone could feed about 800 million more people “if all the grain currently fed to livestock in the United States were consumed directly by people”.
More information on this can be found at cowspiracy.com.