Well, but in this particular case… 
Here’s an example of a man killing a buck with his bare hands. Spooky.
In this hypothetical situation, is the human combatant clothed or naked? Because if the human had the benefit of some thick-soled workboots, his killing power would increase significantly. Just kick straight at the head of whatever you’re fighting until you knock them out, then break the animal’s neck.
I have it on good authority that a raccoon is surprisingly hard to kill in one-on-one combat.
Many things are easy to kill, once you get your hands on them. The hard part is, of course, getting your hands on them.
Obviously you have not run up agaisnt this rabbit!
If you say 1 vs 1 and “bare handed” are you implying you would have no man made advantages over what you were born with? Because you would need to specify whether you are wearing clothing. Clothing can be used as shielding or a makeshift weapon, meaning if you have clothing, you aren’t necessarily barehanded. Now if I was naked in a life and death situation with an animal, I’d be too busy protecting my junk to do any type of damage which would kill the animal.
I have trouble with this whole concept.
I am not going to kill anything with my bare hands. Not philosphy, intelligence. Even in an unplanned combat with something I decide to kill, I am picking up a rock, or a stick, or something, and using that.
I might defend myself with my hands, although I think feet would serve me better. I can come back later with that stick I mentioned if the critter still needs killing. In addition to sticks and rocks, I am going to involve terrain features if I can, and my old pal fire. Speaking of pals, I know some other people, and I can get rocks and sticks for them, too.
Asking me to not use my brain, which is my best weapon, is like asking the lion not to use his claws.
Now, if you want to call it sport, then, no thanks, it’s a cruel, brutal, stupid sport. Maybe as bad as hockey.
Tris
Hey, thanks everyone for the great answers. I now know where I stand in regards to fighting power among the animal kingdom.
But, what if I wanted to fight a lion? Am I pretty much boned? I mean, let’s say I’m taking a walking tour in the Savannah and this insane lion starts sprinting towards my group. What do I do?
I won’t try to lay out the odds on this one, but I would say your time would best be spent in dropping your trousers and kissing your sweet ass goodbye. 
Run faster than the other guy.
Or you might climb a tree, if one is available. We’re not the world champion at climbing, but we’re better than most critters. Meanwhile, while you’re up the tree, you use your cell phone (there’s that world-champion brain) to call for a ranger with a really big gun (brain again).
And depending on just how insane the lion is, you might, just might, have a slim chance of being able to fight hard enough to convince the lion that there’s easier prey about. Though that’s still a pretty long shot, at best.
Do you have a spear? If so, and you are brave and know how to use it, you should win. If you only have your bare hands, you are pretty well fucked. As Chronos said- you might get lucky. But I doubt it.
The appropriate thing to do is yell “Jesus Christ its a lion, get in the car” and then proceed to get into the nearest automobile.
True dat.
My dad, who is 6’2", and roughly 220 pounds, told me a story of his younger days…
Granted this is anecdotal, and though he probably could have killed the cat, he gave up rather quickly.
Supposedly, as a teenager, he was an asshole ruffian (I inherited a few of his bad traits as well), and for some unknown “ungodly” reason, he tried to “choke out a cat”.
The cat won.
My father, who outweighed the cat at least 10 to 1, lost that fight, and was left with WAY more severe injuries thab the poor kitty.
Supposedly the injuries to my father could have required stiches but he neglected them.
That’s his story, and he’s sticking to it.
Wait, maybe not.
I can’t say “easy” to any of those…
You surely have strength to snap their necks, but this General Question was about “bare hands” they all certainly also have the strength to bite all the fucking way through your hand…
…so yeah, it’s all about “killer instinct”… and the will to survive.
edit: funnily enough, a pet racoon took my dad’s finger off years later.
I would like to rephrase that question to the following (answer if you please):
What is the biggest animal you could kick to death?
130 pound woman? 6th grade child?
OK, I’m going to hell.
Both of those have a decent shot at running away, or getting a lucky blow in; instead you could find one of those super-obese 700+ pound people, and kick them to death pretty easily, since they can’t move around all that much - that makes me wonder, would it be possible to really overfeed a cow or such in a similar manner, thus creating a multi-thousand pound creature that you could kick until it dies since it would be too fat to run away?
Remember when in elementary school, if you said the right thing at the right time to the right kid while he was drinking, you could get him to snork the drink up his nose?
Thanks, you just very nearly did that to me. And I’m drinking a frozen fruit smoothie, so it would have REALLY HURT!
“Where you goin’ with that huge bag of feed?”
“Gonna feed the cow.”
“Again already? You fattening her up, eh?”
“Yep.”
“Gonna eat her?”
“Nope. Gonna kick her.”
…and under the category of Plantary Alignment, I’d just like to add that my iTunes shuffle play just now summoned up the early '90s song Can I Kick It? by A Tribe Called Quest.
There may not be an Almighty God, but there does seem at least to be a Somewhat Mischievous God of small but amusing coincidences