I also think that many of them believe that other people see their activity as an activity that presents great risk for the hunter. But, I don't think most people are fooled. Maybe if they changed the sport such that half the time the large trophy animal died and half the time the hunter died. That might be more impressive. Or, how about creating big game hunting zones and declaring them to be "free fire" zones where hunters would be free to fire at anything that moved, including other hunters? Now, there's a sport!
I really have no objection to hunting by people who eat what they kill. I did some of that when I was younger. Most people understand that.
But, this killing of a really beautiful creature like a lion for no sensible reason is what people find offensive. It's all so gratuitous. Similarly, most people have a hostile reaction to those who torture small animals just for fun. It's just very hard to explain some desires.