The most common operations from which commercially-produced carbon dioxide is recovered are industrial plants which produce hydrogen or ammonia from natural gas, coal, or other hydrocarbon feedstock, and large-volume fermentation operations in which plant products are made into ethanol for human consumption, automotive fuel or industrial use. Breweries producing beer from various grain products are a traditional source. Corn-to-ethanol plants have been the most rapidly growing source of feed gas for CO2 recovery.
CO2 produced at the breweries may very well be the source of CO2 for the beer taps. I think it is safe to say the there is no net gain in CO2 (carbon) in the system.
The CO2 produced from natural gas, coal and other hydrocarbons are another matter.
Also, I don't believe that cow farts increase the net CO2 (carbon) in the system.