This is one of the most retarded arguments the "must be >5.56" crowd puts forth, for a multitude of reasons. Among them:
1. What DMK said - Anatomy, physical ability, etc., are just not comparable. A lot of deer research gets done by colleagues here at the U. Deer are usually sedated before handled, but I can assure you that if they're not, you don't wanna put your money on the man in a deer vs. man wrestling contest. Or even the 2nd guy when he jumps in, and maybe not even the 3rd.
2. What c_yeager and others said. The certainty of a quick kill needs to be greater when hunting. Beyond humane considerations, the goal is to not have to chase the deer all over God's green earth after he's been shot. If the b/g gets up and runs away, you still win.
3. Psych effect of being shot often helps w/humans. In animals, being shot just makes them run, etc. Usally on pumped-up levels of stress hormones. (Tho, drugs etc. can do the same to humans, no matter what they're shot with.)
4. Although "designed to wound" is a fallacy, a wounded enemy combatant MAY help your cause.
5. 1 man vs. 1 deer leaves a lot more in the way of options re the logistics of having to tote around gun(s) and ammo. When I used to hunt, I'd take a belt carrier that held, I think, 8 rds. I coulda carried 8 rds of pretty much any cartridge I wanted, and usually had a .30-06 or similar. If I had to engage/repel a whole herd of deer, rather than seek out just one, I'd prob have opted for something else.
6. Probable engagement distances significantly figured into the selection/development of the .223 which no doubt does best at something less than 250-300 m, depending on bbl length, ammo choice, etc. Conversely, a lot of hunters choose to haul their magnums into the woods b/c they greatly overestimate a) the distance at which they might be able to shoot a deer, and b) most ESPECIALLY the distance at which they think their skills will actually let them hit a deer.
During the time at which deer populations in the U.S. were at their lowest, and deer least likely to be encountered up close, folks were predominantly using lower powered, short-range cartridges. Today, we're literally overrun by deer in many eastern states, and large open areas are increasingly scarce, but the guns keep getting more and more "powerful".