A lot of scientific studies and credible sources indicate that agriculture is one of the major contributors of greenhouse gases. The exact numbers seem to vary a lot, I've seen everything from 8% to 45% of global greenhouse gas emissions.
What makes me unsure how to really interpret these numbers is the fact that the process of growing feed to feed livestock, raising livestock, and then eating that livestock, is a cycle. The very same plants that the livestock is eating has during the course of its growth acted as a sink, i.e. absorbing carbon dioxide from the air. This is totally different from pumping oil out of the ground and burning it, which is (in the relevant short term) only production of greenhouse gases, without the sink.
I would assume that any serious study on greenhouse gases would factor in the entire cycle of absorption through animal feed and release back into the atmosphere, yet none of the studies I have seen say exactly how they arrived at the emissions.
Aside from the fact that oil is used in agriculture, when only considering the actual gases released from animal farming vs plant farming, it doesn't really make basic sense to me that there could be a net production of greenhouse gases - where did the surplus come from?