Incorrect. Animal farming is the single biggest contributor to climate change there is.
This study is from over ten years ago and there have been many studies since then that have underscored it, but it was one of the first search terms that came up:
Global Farm Animal Production and Climate Change
From the study, emphasis mine: "Although much evidence has been amassed on the negative impacts of animal agricultural production on environmental integrity, community sustainability, public health, and animal welfare, the global impacts of this sector have remained largely underestimated and underappreciated. In a recent review of the relevant data,
Steinfeld et al. (2006) calculated the sector’s contributions to global greenhouse gas (GHG) emissions
and determined them to be so significant that—measured in carbon dioxide equivalent—the emissions from the animal agricultural sector surpass those of the transportation sector."
Here's a much more recent report that concludes that diets are the main determinant of greenhouse gasses:
Published in Science Direct
Here's an article that cites a study published in The Journal of Ecological Society that estimates as much as 87% of greenhouse gasses are produced by animal agriculture. I left it in the article instead of linking to the direct study b/c I think you need to read some of the commentary and history of why this study was done, namely, that it has been common knowledge for some time that animal farming has been the chief culprit in greenhouse gasses, but that the extent of it has been vastly underestimated.
https://thebeet.com/animal-agriculture-may-be-responsible-for-87-of-greenhouse-gas-emissions/