First, predation is *very* different from aggression; carnivores are basically just trying to make a living, not show their prey `who's boss'. Meanwhile with [healthy] aggression, the intent isn't even to hurt, let alone kill. It serves to resolve social conflict and clear-up heirarchical ambiguities. Thus highly competitive friends can remain friends and sparring partners [and hunt cooperatively, for that matter], by coming to see each other as equals, falling into a stable `hero&sidekick' orbit, or -- best of all -- switching dominance depending who's better at what.
Second, warfare is a bit of both, so it's not a natural fit for most. You have to fuck people up to some extent, to make decent soldiers out of them -- jointly increase their `team spirit', selflessness and social cohesion with insiders, while also *decreasing* their ability to see outsiders as human [reduce them to `prey' basically]. A soldier afflicted with empathy won't shoot the enemy, but a soldier without empathy won't do shit for anyone on their own side either -- so both are useless.
Third, modern humans suck at hunting for lack of practise, basically [like you said]. Cat's who've been raised indoors kind of suck at it too, btw, because mice and birds are *way* more perceptive than a ball of fluff on a string. ;-P
* If you've seen cats playing together, you know it's only `practise hunting'; they *always* stop short of killing each other.
* If you've seen cats hunt, you know it's *not* playful; it's dinnertime.
* And if you've seen cats fighting, you know it's not playful *or* homicidal. It's `fuck off', basically; neither wants the other animal to stick around, not for playtime or for dinnertime, just go away, now.