The iconic phrase “Brains!” associated with zombies is most famously from the “Return of the Living Dead” series. This horror-comedy franchise, which started with “The Return of the Living Dead” in 1985, diverged from traditional zombie films by featuring undead creatures that specifically vocalized their craving for brains. This particular depiction of zombies was a departure from earlier representations, where zombies typically didn’t speak and were not specifically focused on eating brains.

There is no singular zombie lore. The brain eating entered pop culture with “Return Of The Living Dead”. That movie and the associated Living Dead series exists as a result of an IP fight between John Russo and George Romero. It is not canon with the George Romero zombie movies (Night Of The Living Dead, Dawn Of The Dead, Day Of The Dead, Land Of The Dead, and the lesser following low budget movies).

In Romero’s movies the zombies do not go after brains, they don’t say “brains”. Their hunger for human flesh is discussed by characters but nobody really knows for sure why zombies attack or eat people.

In many other zombie series, there are often theorized reasons for their behavior, but rarely a solid answer, and very few series have zombies that explicitly want brains to eat.

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I think everyone has already covered the fact that it depends on which kind of zombie you’re talking about, since the only “real” zombies aren’t actually undead at all, and are certainly not mindless.

But! Even within the brain hungry zombie type, there would be plenty of reasons to target something other than the head!

First, the chances of attacking a living person, getting through their skull, and to the brain in a single attack are low. So, attacking other parts of the body in order to prevent the prey from escaping is a good idea.

If you then assume that the zombies will want living brains, rather than freshly dead, the guts are the ideal target. See, if you can get the living human down, and tear into their guts, they’ll be immobilized for the most part, but their heart should stay beating for at least a few minutes. This gives your brain eating zombie much better chances of having a bit of live brain. So, even if they’re too weak to crack the skull and eat quickly, if you have time, you can make it happen anyway.

Now, you probably were seeing one of the varieties of zombie fiction where their hunger is for either flesh in general and human by preference, or specifically for human flesh.

The walking dead zombies were flesh eaters in general, they were shown to eat deer and horse for sure, but seemed to prefer human when available. And there were a good number of scenes where they were seen digging into the abdomen. While Robert Kirkman has never given real details about how and why his zombies function as they do, we know two things for sure: First, they can function even when their body isn’t fully intact; second that they have a constant hunger for flesh that will drive them to attempt to eat, no matter what happens to the rest of them. Indeed, severed zombie heads can still try and eat.

So, you run into zombies in that world that may not be at full strength, but can drag down the living in numbers. They then crawl their way to the meat and gnaw.

But, the reason why walking dead zombies often go for the soft parts rather than arms and legs isn’t an in-universe thing, it’s practical. Zombies tearing the guts out of a victim looks cooler, and it’s easier to make effects for. Making a believable leg eating prop is a lot harder.

There’s also been versions of zombies where they have residual capacity for thinking, and memories. When that’s the case, you could be dealing with the mind that’s left going for a target that’s easier to chew into, as compared to a skull. The throat and belly are the most vulnerable targets available for human teeth that will kill or immobilize in a reasonable span of time.

Zombies aren’t real. And will take on any qualities the writer wants. Some people write zombies as brain eating mindless undead. Others are super fast group thinking infected humans. It’s all up to your imagination.

If you would like to hear it from the zombie’s perspective

https://freemusicarchive.org/music/Jonathan_Coulton/JoCo_Looks_Back/Re_Your_Brains/

Most zombies aren’t Anatomy majors.

Well if they had any brains, they’d crack open the head, but they’re famously short on brains

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We’re talking about zombies here bro, it’s not like logic has any place here.