Zombies vs. animals? The living dead wouldn't stand a chance

“Unless suitably armed”. Humans are brutally effective pack hunters and killers, and smart enough to back up lethal force with habitat modification, sophisticated logistics, and other tools necessary to turn initial violent success into increased population in ways that other predators can only dream about (well, actually, most of them probably lack the cognitive capacity, which is why they can’t). However, (in part because of this) a huge percentage of humanity engages in little or no violence and mostly deals with absurdly specialized functions that become dangerously irrelevant if society experiences more than a slight disruption.

A hypothetical zombie plague would not be an extinction-level event(since zombies are dumb, zombies have finite lifespans, and kill-teams from uninfected areas would find them easier to exterminate than even unarmed civilians, because they are dumb, heck, just put some live bait in a secure cage and then drive around in an armored bulldozer or other closed vehicle, squishing and squishing…); but your average Joe is probably unprepared for a fist fight, much less a grappling contest with a humanoid that feels no pain or fear, suffers from no blood loss or shock, and just has to land a single bite in order to doom him to a particularly messy death.