Especially as depicted in movies, video games and comics. The zombie virus spreads extremely rapidly and infects most of the population in a very short period of time. The remaining survivors spend a long time being surrounded by zombies that for some strange reason stop spreading rapidly and suddenly for every hundred zombies killed one person gets infected.
1. The method of transmission doesn't allow for the spread of the virus as needed: In virtually all cases (save for a very few like Resident Evil) the method of transmission of the "zombie virus" is biting. Even those stories that allow for a different method of transmission (usually airborne) then change it before the story really begins so that it reverts back to the bite. Now I Am Legend did attempt to rectify this by stating that stating that even though the virus was airborne there was a certain percentage of humanity that was immune. The problem of course is that if you're immune to the virus while it's airborne then YOU'RE IMMUNE TO IT ALWAYS. Biting doesn't change that. Unless the virus mutates until it's method of transfer is changed but that takes time. A long time and considering how many zombies get slaughtered and how often it's just not possible for the virus to transmute much less infect new hosts.
2. Viruses that act quickly are quarantined in small populations: What this means is that an virus that has a short incubation period (which is required for a zombie apocalypse) causes visible symptoms in it's host usually before it's had time to transmit itself to another host. This is why quarantine is so effective for stopping the spread of certain communicable diseases like Ebola. A patient who suffers symptoms very rapidly is identified with minimal contact with non-infected persons and separated before the virus can obtain a large number of hosts. This is not only scientific but historical fact. Throughout history the viruses that have the longest incubation periods are the ones that cause the most death are most likely to spread to large populations before they can be contained.
3. The most successful viruses don't kill you: "But zombies are UNdead." you say? Here's the problem with that. Most cases of deaths due to illnesses aren't necessarily from the virus itself. Take the HIV virus for example. No one has ever died because they have AIDS. No one. Not one person. AIDS (Auto Immune Deficiency Syndrome) just causes your immune system to shut down. Once that happens new viruses and bacteria can move in and cause you suffer illnesses that your body would otherwise easily fight off. Because your immune system can't do it's job any foreign bacteria can take over to the point where they kill you. Viruses that kill quickly are rare because the host very often dies without infecting new hosts. Now there are certainly viruses that can be transmitted from a deceased host but how many of us interact with the dead? Very, very few. Most of us see a dead body and immediately get away from it as fast as we can. This is why the overwhelming majority of viruses are transmitted from host to host while the victims are still living.
And don't even get me started about how any virus that exists that mimics this kind of behavior kills the host in days. Don't waste your time with your conspiracy theory nonsense about the government making "super viruses" in bio weapons programs. You're full of shit and I don't need to talk to your friend "who is well connected" to know that.
The zombie apocalypse isn't real. It's a plot device meant to tell a story. Nothing more, nothing less.