Ok, picture this.
A man has a heart attack, alone at home. A couple of friends were coming for a visit. They see his body lying on the floor, and break into the house to help him, but get bitten in the process. That's already 3 zombies
They get bitten... and ? it's 3 against 1, they could easily take him down.
What I mean is that pretty much every death would become 2; you'd see people getting attacked because they didn't know if a man was a zombie or just sick, and you'd see random killings because someone thought another person was one, when he actually wasn't. Cancer patients would come back to life and infect their doctor/nurse. Firefighters would get bitten while trying to save people.
Which is a matter of numbers and adaptation, the zombies might get everyone by surprise first, but the whole thing could be put back into control again.
Not to mention, they take some time to become walkers. Just imagine a war, not everyone who dies in one gets shot in the head. Even if everyone knew about the disease already, the soldiers wouldn't have time to burn every body/wouldn't have ammo to shoot everyone again. You'd see random walkers, wandering into nearby villages, infecting and eating everyone.
Then don't wage a fucking war in the face of an obvious crisis ?
Problem is, you're assuming everyone would be stupid like in the show, which isn't the fucking case, obviously, otherwise the human race would't have survived it's early years.