The idea that animal ag is a major contributor to GHG emissions (many people still believe the ridiculous claim of 51% worldwide) comes from retracted reports from the FAO that were shown in propaganda movies (what the health/cowspiracy - both by the same 'activist' director Kip Anderson) where they compare animal energy inputs (moment its born to the moment it goes in your mouth) only to the tailpipe emissions of the energy industry and transportation. Frank Mitlohner showed how these studies the comparisons were wrong; the studies were since amended to much lower numbers, but the cat was out of the bag... and the movies stayed the same. Frank Mitloehener did a great job at pointing out the problems in the reports, leading to a re-calculation. http://theconversation.com/yes-eating-meat-affects-the-environment-but-cows-are-not-killing-the-climate-94968
They also count animal water as consumptive only, ignoring that they piss out or transpire the water, thus; recycling it (especially on pasture) back to nature, so they'll say 'cows use xx gallons of water. Cows don't 'use' water, they consume it then excrete it. Methane from cows is a flow-through gas, meaning that it is not accumulative (unlike fossil fuel based methane), but rather part of a cycle (like the normal carbon cycle in nature - think trees growing, rotting, turning to CO2 then taking in CO2 to produce cellulose based trees again).
Cows replaced large ruminants of the past, the ones that were market hunted to near extinction in the US/Canada. The US/Canada by far are the worlds most efficient producers of food cattle (Aussie/NZ do good too). Feed lots are not the best thing if you care about animals more than people; they are also quite unsightly, but they sure are efficient.
Cows are awesome. Let's continue to improve the process, but cows themselves are not a 'problem'. If we start eating foods that are 1/2 as nutrient dense and bio-available (plants), then we will need twice as much food, most of it trucked in from far away, and keep in mind that the majority of food waste comes from plant foods. Also, to wind down this too-long post, keep in mind that ruminant animals largely thrive on feed that is not suitable for humans. We generally do not compete for resources. They can grow in the forest or on grass land, in semi-arid conditions, and fertilize the soil. Humans can't eat trees or grass and plants need animal fertilizers (or mined chemical fertilizers) to grow.