We've had cows for a few thousands of years but never that many, never a population of cows made to feed a population of 7.5 billion humans. Just like all the components of anthropic global warming, this wouldn't really be a problem if we had simply kept our population to 200 millions like in the Middle Ages.
That being said, the "cows cause global warming" argument is actually very fragile. We don't have any reliable estimate of how much cows contribute to global warming, and even defining what "how much" is, in scientific terms, is actually a very non-trivial question leading to many very different definitions, and therefore very different numbers (including estimates which claim that cows actually *reduce* global warming). The vegans always cherry-pick the worst numbers, and media usually spread those because it's a good way to make the headlines.