As always, when these topics come up, I'm struck by a quote that came out of a Cracked article of all places. "A zombie's apex predator is also that zombie's only food source and its only means of reproduction. This is like having to wrestle an adult lion into submission every time you want to have sex or eat a sandwich."
If a zombie eats its victim - particularly their brain, which all zombies apparently crave - bam, no new zombie, and mindless zombies aren't going to just stop killing/eating someone once they have suffered just enough damage to become a zombie in return. If the zombie bites someone but that person manages to kill the zombie before they succumb, net zombie population change=0. One human being who manages to kill two zombies before they are infected=-1 net zombie population, and the ratio just gets more unfavorable from there when we start using guns and defenses.
Humans are the deadliest things on planet Earth, and it's not because of our physical traits. It's because we are smart, sneaky, ruthless, tool-using sons-and-daughters-of-bitches, everything that a shambling corpse is not. You basically have to make a zombie a magical super-monster that ignores both physics and biology to result in it being any sort of threat. There is a very good reason almost all popular zombie stories (Walking Dead is a good topical example) only start 'after the end', because showing the end itself would be incredibly unrealistic. Stack on the fact that we are innundated with zombies in popular culture, and the odds of any Patient Zero managing to start any sort of outbreak is basically fantasy. I love post-apocalyptic stories, but zombies are pretty much the one flavor I just can't take seriously enough.
I'd be more scared of a mass uprising of murderous cows than a zombie plague. Cows are smarter than zombies, and much harder to incapacitate. And they outweigh the total humans on earth, in terms of body mass, by a significant degree.