Aw, c'mon guys. Even the most deluded zombie fan knows it is just a fantasy situation and that actual science is not really the point. What makes fantasy fun is the suspension of disbelief and pretend reality. Fiction, remember? It would be fun if it was real, but we can only wish so much.
Ah, you probably missed the explanation in several movies of one being zombies are the revived dead and all of the brain's higher functions such as thinking, speech, reasoning, math, etc. are gone and all that is left is their most primitive, base instincts like locomotion and eating. That's because in the process of dying, the most complex of neural functions tend to disintegrate more rapidly than your natural, primitive ones. Therefore, the only neural functions left are the ones that are normally hard-coded into any living thing, which are the default, primitive ones.
On why they prefer living meat is that zombie meat are tainted by the same viruses that animates them (if the supposed cause is pathogenic in nature) which they can smell and tell themselves apart form the living. In the case of the Walking Dead series where the survivors spread zombie bile on each other to make them smell tainted, dead, zombiefied and generally unappetizing to all zombies. Or that the zombie flesh is basically dead and lacks living tissue which for whatever reason, nourishes the dead so they can keep on shambling and muttering "braaaiiinnnsss..". And it could also be a means of how they
multiply themselves, by tainting the living and create new zombies.
Note that this rationality is not applicable in Night of the Living Dead where the dead becomes zombiefied with no apparent reason. Their only explanation for the outbreak was a biblical one, where when the pits of hell becomes full, the overflowing dead will walk among the living. And they eat people, to create more of themselves. Generally, it's a simple plot to wipe out humanity or else it would not be pertained to as a zombie-type "apocalypse".
Then again, if zombies just simply shambles about aimlessly and hilariously bumping, tripping themselves on numerous immovable objects with no intention of doing any sort of horrific act on the living then that would just simply not make a good scary movie wouldn't it? In the end, it's because the writers says so.
