Yeah, I did some more reading about it and if I'm understanding correctly, the main issues are from the machines involved in the process (eg, fertilizer production chain, farm machines used to plant, grow, harvest, and process the feed crops, transport of the feed and the animals) and the carbon being converted to and released as methane from the cows themselves.
Chickens and pigs aren't as bad because they convert their calories to meat more efficiently and chickens don't release as much methane from their digestive process (not sure about pigs, didn't dig that far).
Land use is another issue, though that's more for biodiversity than climate change. Though all the land that used to be forests did contain some of the carbon, even if it was just temporary, new trees would replace the old in forests but that doesn't happen in pastures.