Honestly, it makes a decent argument. The trouble is, most zombie movies rely on some form of magic or another to move the plot forward. Unless there is sudden and dramatic shift in the fundamental operation of a zombie body, which would involve nothing less that the sudden evolution of new cellular structures in the billions of cells in the body during the always brief period from exposure to zombification, you'll find the human body needs oxygen and glucose. Some tissue in the human body can operate without oxygen (notably most of your muscle tissue) but the process results in incredibly harmful byproducts (lactic acid for example). This basically means that any interruption of the circulatory or respiration systems of a zombie body ought to have the same impact as it has on a normal human.
In much the same fashion, if we assume that the zombie is "dead" by traditional means of determining such things, one would still find that there are some very basic tenants that the body must be followed. Regulation of vital functions would still likely be centralized to an extent even if it were through some newly grown organ. Said organ would still need a way to communicate with and control existing tissues in order to do things like move the shambling/running corpse around. It would still need a way to gather and parse sensory input. There are only two plausble explanations for this: Either the zombie rapidly develops entirely new systems overnight or it just uses the exact same systems the normally functioning human used in the first place. The former is just shy of impossible: the growth of significant new body structures would take more time and metabolic energy than could reasonably be expended in the space of a few hours or even days. The latter is far more reasonable and would mean that anything a normal human is vulnerable to a zombie would be too. This would mean things like vulnerability to nerve agents and at least some complications from sudden nerve stimulation (flashbangs, intense pain etc) as such things can simply overload the nervous system.
The basic point I suppose is that the zombie of movie and often video game fame relies on some magical process that allows for incredibly limited vulnerability. The more realistic portrayal would be something on the order of 28 days later where there was no actual physiological difference between an infected human and an uninfected human. And, for those who somehow think that simple weight in numbers would be sufficient to win the day against humanity, remember this was the same sort of thinking that people had in the first world war and it never worked out the way they might have thought. A zombie plague as portrayed in movies is only a threat to humanity if humanity refuses to work together in the time of crisis. Even in the worst case scenario one could imagine, where a huge portion of the population is turned before people figure out what is going on, the odds of total zombie victory are slim at best as even relatively small and dispersed military units could move quickly and efficiently through areas causing massive casualties to infected individuals as they go until such time that they could link up with larger units. Search and destroy operations would quickly quell the largest collections of the infected and normal attrition through any number of means would spell the end for the rest in short order.
