Symbolism, Imagery, Allegory
Coriolanus is always running around calling the plebeians names like "curs" [dogs], "hares" [kind of like rabbits], and "geese" (1.1.168-172), like just in case they didn't already know that he thinks they are so cowardly and lowly that they're not even human.
Of course, the plebeians don't think much of Coriolanus either. Among other things, they call him a "dog to the commonality" (1.1.28-29) when threaten to kill him. Yet, as Menenius points out, when the plebeians call for Coriolanus' death, they're basically acting like a bunch of "hungry" wolves who would like nothing more than to "devour" the guy (2.1.9-10).
Some literary critics think that a lot of the animal imagery is a shout-out to one of Aristotle's famous sayings: A man who is "incapable of living in a society is either a god or a beast" (source). And, sure. We can see how that might apply to Coriolanus, who's a lot like a "lonely dragon," incapable of living among Roman society and speaks "a' th' people / as if [he] were a god, to punish; not / a man of their infirmity"(3.1.8082).
Then again, maybe he's just trying to remind us that life in Rome is brutal and violent—even animalistic.