I'll be 45 this hunting season. I bow hunt, and I hunt with a 12 gauge shotgun (plus a .22 or 410 for small game, and occasionally a 20 gauge.) I shoot deer every year. In all my years of hunting, I have only ONCE had a deer drop in the spot where I shot it. And, after I shot, the deer just stood there for what seemed like an eternity - I thought I missed, took careful aim, and shot again! It continued to just stand there. As I was about to pull the trigger for the 3rd time, thinking something serious was wrong with the aim on my gun, the deer finally collapsed right where he was standing. Both shots were in the ideal placement. Other than that deer, the average deer runs at least 30 yards before dropping. The last deer I shot was a double lung shot (you do NOT aim for the head, you do NOT aim for the heart.) It ran off with multiple other deer that were around it. When I started tracking it, I could tell from the type of spray/color of the blood that it was a lung shot. Within 10 yards, there was no more blood. With all the other deer tracks criss crossing, I had to retrack it multiple times before I followed the correct set of tracks. At a guess, I'd say it went for 5 to 10 seconds. At the speed a deer runs, 5 to 10 seconds can be a considerable distance.
My first year of hunting - zero deer. My second year of hunting, I was slowly stalking through a thick area. I saw a big buck stand up and look at me from behind a large fallen tree. All I had a view of was his neck and head. I had been taught not to take a head shot, but I did anyway. 12 gauge shotgun. I spent the better part of an hour tracking that deer before I was able to take a kill shot. It would almost certainly have survived the head shot.
I've never seen, but have heard occasional stories from friends about deer they had put out of their misery - idiots (like me with my first deer) had taken a head shot. Mine had merely glanced off the skull (but apparently giving him a concussion or something, because his behavior was very weird.) But other head shots gone wrong can lead to a jaw shot off, or half a face shot off, with the animal surviving until it starves to death or something. Not humane at all & why you do NOT aim for the head, at least not on the initial shot.
As far as a compound bow being for sissies? Whoever said that is also ignorant, especially if they're going to advocate for a clean kill & would support the use of a gun. Compound bows are more accurate, less susceptible to accuracy changes due to weather related factors, and shoot faster. It's nice for the arrow to get there before the animal moves much. As far as the humaneness - an arrow will punch right through a sandbag that would stop a slug. Arrows kill by cutting and bleeding, rather than by blunt force trauma. Most shots go in one side and out the other. I had one friend relate how he shot a deer with his bow; the deer stopped for a second, put its head back down to continue browsing, and about 5 seconds later, just fell over. It hadn't even realized it had been shot. If your only experience with compound bows is bows in a high school gym class that are dialed in so that kids can draw them back, then I have no doubt you think "anyone could draw it back." I took my bow in to where I worked once. Only ONE of the guys working there could draw it back. All of the bow hunters I know put considerable time into practicing with their bow. In fact, far more time than they put into practicing with their guns. But, I don't think some of you understand quite how powerful modern compound bows are and how well they transfer the stored energy into the arrows. Do you think a sheet of plywood would make a good back stop for a bow? Once upon a time, I thought so. An arrow went through a filled box target, penetrating right in a corner where the foam wasn't packed in tight enough, exiting the box, hitting the plywood, passing cleanly through the plywood, hitting my garage door, putting a hole through the door, and lodging in a 2x4 on the other end of the garage. I took a shot at a walking fox last year and hit a small dead tree (too focused on the fox, and as I was swinging, I never even noticed the tree), about 4 inch diameter. It split off a huge hunk of the tree. Compound bows are very deadly weapons.