2415-2418 in the Catechism seems to cover the morality of hunting quite well.
Part of the issue is seems to be that we tend to romanticize and anthromorphize animals in our culture – every kid has a few cute stuffed animals sitting around when they’re young, and these become formative images. When we get older, we learn about the reality of animals, but have something of a cognitive dissonance between what we felt as children and what we know as teenagers or adults.
It also seems we could draw a parallel between the respect and regret at killing that hunters have with saying Grace at our meals – we understand that our daily sustenance is dependent on many things and that we are grateful to have it. A hunter understands that their bounty (one deer can provide quite a bit of meat) comes at the cost of life.
Finally, I don’t have a problem with teaching children how to hunt. We have become so disconnected with the real world in recent generations that we are losing the division between internal and external activities, which can’t be healthy on any level. Additionally, it often builds a sense of self-reliance and confidence that is also on the wane, as well as teaching skills which may allow a person to survive in an emergency or time of difficulty.