It's too early to call the Swine Flu an epidemic, but I'd like to take this opportunity to remind readers that most epidemics throughout human history have originated from domesticated animals.
Measles, smallpox and tuberculosis came to humans from cattle, and the flu originated from pigs and ducks (including the avian flu). Whooping cough (pertussis), which causes 600,000 deaths per year worldwide, comes from pigs and dogs.
Interestingly, it doesn't appear that SARS originated from livestock, but instead from civet cats; that said, the first diagnosed patient was a farmer from Guangdong Province, China.
So not only would the elimination of livestock work to reduce climate change, it would dramatically reduce the chances of diseases being transmitted to human populations.