You hit on a couple arguments that hunters get thrown at them regularly by anti-hunters. It goes something like this.
If a hunter uses a rifle and scope. The anti-hunter does exactly what you are doing here and saying "that's not brave" that's not "sporting", "they should use a knife".
If the hunter actually uses a knife (yes this happens). The anti-hunter replies with something in the vein of "that's barbaric", "that's inhumane".
The only conclusion that I and many hunters can draw is that the vocal anti-hunting crowed is largely arguing disingenuously. There is rarely any effort to actually understand what hunting is and how it works, they just knee jerk from one emotional reaction to another even when it's entirely inconsistent. Emotion over reason.
I do acknowledge that you are at least asking for the explanation, which I can't personally give you for the kind of hunting you are talking about (which is a tiny fraction of what constitutes hunting) since that's not the kind of hunting I do.
But even the kind of hunting I do I get the irrational emotional backlash. My hunt starts months ahead scouting areas, getting a feel for the routines of the animals there. By season open, I might have laid down as much as a couple of hundred miles, preparing for this one day on this one particular hunt. On a typical weekend hunt, I'll cover 20 miles of mountain terrain (as much as 6000' elevation gain loss) humping a pack and if successful on something like an elk, I'll then spend the better part of 24 straight hours, on top of whatever I walked that day, packing the animal out. And still I have, pardon my french, jackasses, try to compare what I'm doing to target practice on bambi.
I can without a doubt in my mind state that I know and know more intimately, the areas that I hunt than any of the people who would give me a rash and a shit for it. I have been up every ridge and down every valley. I've baked there on hot days and froze there on cold wet nights. I don't just know that there are elk there, I know the elk, I recognize the individuals and they no doubt recognize me, or at least my smell. I've got names for some of the bears and I can tell you where the mountain goats will probably be just based on time of day and weather.
Hunting is not an unnatural act, shopping is an a natural act. Hunting is the closest most modern people will ever get to truly living a natural life.