You are going to eat me? So are bears.
Zombies are dead people who get up, shuffle around and try to eat our flesh, our brains, or sometimes just chew on us until we turn into zombies ourselves. Being devoured is scary and all, but there are dozens of animals who eat human beings, they are way more efficient in how they go about it, and they're also REAL. If I'm gonna get scared because some shambling mess of a zombie wants to "tear the flesh of the living," he's gonna have to get in line behind sharks, bears, crocodiles, and giant snakes.