Without question, a booming worldwide population and the need to feed them have resulted in greater greenhouse gas emissions.   The goal of any civilized society has always been to make food affordable to everyone regardless of income and we are converging on that rapidly.   If anything, the rising obesity problem is because we are reaching a Utopian ideal of enough food for everyone in richer countries.

But the greenhouse gases from food production are a concern and one proposed solution by a group of economists in Sweden is to increase taxes on meat and milk (but not fruit and vegetables, far bigger industrial polluters than meat and dairy, which will make the vegetarians happy), meaning poor people will be able to afford less and farmers will make less.    
Because these are economists their logic is simple; taxes of €60/ton CO2eq on meat and milk could reduce greenhouse gas emissions from European agriculture by around seven percent.  As I have done in the past, the daisy chain of these spurious percentage numbers usually leads to someone claiming it and a flawed model behind the results but people wanting to believe it and so they shelve their skepticism.

Even more speculative, they assert that if the dairy and meat farmers then convert their land to bio-energy production, the decrease in emissions can be six times greater, though where they got that number is a question since no bio-energy is carbon neutral yet.  Perhaps, like the 'gallon of gas per pound of beef' claim by one vegetarian and '140 Liters Of Water In My Cup Of Coffee' claim by a 'virtual' water advocate, the numbers are made up but because they have an air of truthiness to other believers, it gets repeated and data mapped to those beliefs.

In the article, these economists state that reduced meat, milk and egg consumption will significantly lower emissions of methane and nitrous oxide, which is absolutely true, since methane has 23X the effect of CO2 on warming and nitrous oxide, while only 9% of total greenhouse gas emissions, has 300X more global warming potential than carbon dioxide.

Any physicist or botanist knows their logic is flawed.  If methane is the big problem it is plants causing it more than cows that fart(edit - sorry, ruminants, I had a rant about farting termites and started making cows and sheep fart, but their methane is belching) too much.   If we cut down the Amazon rainforest, for example, methane production would practically disappear but anyone with common sense would object to such a data snapshot in a complex ecosystem, much like I object to poor people being forced to become vegetarians.  

And that is what they are doing - actual emissions from the meat industry are impossible to measure so they instead want to try and make social engineering look scientific; 'changing' food habits, which again means people with less money, are where they want to focus.    Despite a complete inability to measure greenhouse gas emissions from the meat industry, which they concede, the researchers cite as fact that if beef is replaced with beans  the reduction is 99 percent.

"A tax on the emissions from food production would normally be preferable. But as this is virtually impossible in practice, and the effects of switching away from meat and milk are so great, we show that it can be far more effective to apply the tax directly to the meat and milk consumption," says Stefan Wirsenius, co-author of the paper and a researcher in the Department of Energy and Environment at
Chalmers University of Technology.

Beef would be taxed higher under their proposal while chicken and pork would be taxed lower as their emissions are lower.  Non-flesh farming would be taxed nothing.

The fact remains that more taxes are a regressive solution to a problem better solved by science.   Given the chronic fixation on mitigation and rationing that advocates of this approach have, we must conclude that there would be no society at all if they ran things in the ancient world; in the ancient world, when hunting got sparse, economists would have argued for taxes on hunting.   Ancient scientists invented agriculture and learned how to domesticate livestock instead.

Engineering cows that burp less, and better energy sources, is the solution to greenhouse gases, not making poor people tread water by having their taxes for a decent dinner go up as their income does.

Citation: Stefan Wirsenius, Fredrik Hedenus, Kristina Mohlin, 'Greenhouse gas taxes on animal food products: Rationale, tax scheme and climate mitigation effects', Climatic Change