A .223 will kill a deer, usually, eventually. But that's not how we hunt. If you are in need of food and have nothing else, you'd shoot it with .22shorts as in H4831's example or snare it or club it if you could. But for "sport" hunting, we are trying to get a humanely quick kill with one shot to the vitals, so hunting regulations tend to require a more potent cartridge that increases the chance of that effect.
As a former professional soldier, I really don't believe that my predecessors who once upon a time had to choose a new cartridge, chose the 5.56mm NATO for the reason that we would wound the enemy rather than kill them, calculating that it would take more resources to extricate the wounded and care for them. I am sure they were aware of that idea, and didn't think it was entirely worthless, but the primary goal of having an individual soldier shoot an individual enemy combatant is to take that individual enemy out of combat, whether wounded or dead. (We teach our own that to help our wounded we must win the fight, so we don't rely on the enemy to stop fighting immediately to care for his wounded. By the time he diverts the extra resources to care for his wounded it doesn't help us if we are already defeated.) The secondary objective is to at least disrupt the enemy's activity, by making him take cover.
There is always a compromise. Although a bigger bullet with more energy would be more effective if it hits, the 5.56mm offsets that advantage of larger cartridges in more than one way. Being smaller and lighter, the individual can carry significantly more ammunition and the logistics system can supply him with more ammunition, which means more opportunities to shoot the enemy or at least keep making them take cover so that they can't shoot you or maneuver. And compared to previously used larger cartridges, it is easier for most people to shoot accurately (wounding an enemy is certainly better than missing him, even if it doesn't divert other enemies to care for him) with the lighter weapons and lower recoil that is possible with the 5.56mm cartridge , so that also increases the opportunities to put enemy combatants out of combat, whether by killing or by wounding them.
So the 5.56mm is believed to be effective on humans because it can achieve these things - rather different from what we would want it to do to a deer.
