The EPA doesn’t place livestock as the leading cause of GHG.
https://www.epa.gov/ghgemissions/sources-greenhouse-gas-emis...
Livestock are an important source (just not the most important). Documentaries with an obvious angle also purposely edit their footage to cast their villains in an unflattering light.
There’s also a good blog post by the Union of Concerned Scientists about this very claim.
https://blog.ucsusa.org/doug-boucher/cowspiracy-movie-review