You exhale carbon dioxide. However, this carbon dioxide comes from the carbon in the food you eat, and the food you eat obtained it from the atmosphere. Thus, it's a cycle. As a system (ignoring food transportation, deforestation, etc.) it's effectively carbon neutral.
By contrast, when we dig up oil and burn it, there is no cycle. It's a one way street.
Methane production from cattle is slightly more complicated instance of a carbon cycle. The cows produce methane, which is a more potent greenhouse gas than carbon dioxide. However, it degrades in the atmosphere into C02. Since this C02 was obtained from the food the cattle ate, this is another cycle.
Since the methane released from cattle is continually degrading, it does not accumulate. The total amount of bovine methane resident in the atmosphere is ultimately a function of herd size, or perhaps more accurately quantity of feed consumed.
You may be surprised to learn that cattle herd size has remained relatively stable over time. Additionally our planet was once host to wild ruminants like Buffalo which no longer exist in large numbers. As a result I would be very surprised to learn that bovine methane production is completely out of historical context.
As a result I see this as a topic which generally serves to distract from the root cause and real problem associated with climate change - fossil fuel usage.