OK, I'm going to try and give a serious answer on (my take of) A Silly Question (because Zombies aren't real- you did know that, right?)
There are parasites that radically alter the behavior of the host organism- there was even a write-up I read on a "Zombie Parasite" that infects ants in the rainforest- it makes the infected host climb as high in the trees as it can before dying, so it can be spread by the host being eaten. Apparently, IIRC, the predator bird that finds and eats the infected ant doesn't normally get them as a snack, because they (the ants) normally stay at ground level, or quite near it. The predator bird eventually dies, lands on the ground, and is eaten by- you guessed it- ANTS!
There are viruses that also cause noticeable behavioral changes in the infected host- Rabies has already been pointed out as a good example. It's not TOO big a stretch of the imagination to envision a virus that makes the host seek out more biological material to infect, in the case of a zombie, other human beings. It would also make sense that if the virus can thrive in a human being, then causing the host to seek another human would be in the best interests of the virus- it could reproduce in a hospitable organism. If rabbits were vulnerable to a "zombie virus", but humans were somehow naturally immune, rabbits wouldn't waste the time and effort biting humans, they'd bite other rabbits.
Suppose the zombie virus did not so much ACTUALLY re-animate the dead, but gave it's victims more of the LOOK of being "undead"- this would mean a working digestive system, so a craving for food, coupled with the virus' "mandate" to replicate in another human would give you the scenario of infected humans biting other humans. And, why does a head shot destroy the zombie? Simple- it works on everything with a brain, infected or not. I could easily see this as a movie premise involving rage zombies, like the 28 franchise offers.
Now, I'm going to delve into the quasi-religious, so bear with me- it has NOTHING to do with any religion's beliefs being valid or not, but more of a look at what religion talks about, but from a scientific point of view, even if it is just theory. So save the butt-hurt for the firearms section.
Any form of life, on Earth, anyway, has some form of energy within it, that differentiates the living version of it from the dead version. A plant, an animal, a human being- once dead, is still comprised of the same chemicals, the same cells, arranged in the same manner they were before death. If you were to remove or repair, somehow, the cause of death, you would have what should be a living organism, much like Dr. Frankenstein's 'monster'. He used massive amounts of electricity to re-energize the dead flesh, and grant his creation a semblance of life, if not life itself (depending on a variety of interpretations).
Chemical reactions can, in some cases, emit energy. Suppose a chemical combination were created that would react with the chemicals that make up animal matter, say, one of the proteins found in muscle tissues. It emits, as chance would have it, the exact sort of energy that animates what would otherwise be a collection of dead cells. There you have it- the re-animated dead form of zombies. I could also see a form of radiation, different from anything we've run into so far, being able to re-create that same "Spark of Life"- in fact, if you read the Zombie Cataclysm book in my sig line, the radiation idea in the premise of the campaign was my idea, I just didn't name it, the writer did. Now, if you consider this spark of life as being the soul, which departs at death, would you consider the re-animated dead as "soul-less", or would they have a 'new' soul, courtesy of whatever generated the energy that caused the re-animation? As to why they would want to eat other human brains, I can't imagine- even I have my limits.