Is agriculture really a net contributor of greenhouse gases?
The issue is that it is not always a cycle, when you drain wetlands or burn forests to make more farmland that's not a cycle that is permanent change. A change that can continue having effects for centuries. Then of course you have petroleum fuel used to run tractors and the production of fertilizer which are often not cycles either but pure extraction.  

One of the reason the number varies so much is because of disagreements about what falls under agriculture, does the fuel used to run a cargo ship moving bananas count? How about mining equipment used to extract minerals used to make fertilizer? Many simply forget to include things like peat bogs or changes in soil bacteria. 

For instance draining a peat bog releases tremendous amounts of carbon, as a functioning net carbon sink is changed into a carbon producer. Sometimes this happens as water is diverted to farmland but often it is done just on purpose to get more farmable land. Exact impacts vary from place to place leading to wide ranges of estimations further complicating it.