Hunting pays for the vast majority of conservation work that goes on in the world, folks.
Bows, believe it or not, are extremely efficient at what they do. I haven't shot any 500 pound cats with one, but I have shot plenty of critters with one and I've shot plenty of critters with various firearms.
A good bow shot drops game faster than any rifle shot I've seen short of a CNS hit. I've seen double-lunged deer take a hit, take a few steps, wobble and then fall over with a massive blood stream pouring out of both sides of the animal. Meanwhile I've seen deer shot through the heart with a .300 Win Mag run 100 yards up the side of a mountain and collapse in a heap.
The idea that you can't make a clean kill on a big animal with a bow is silly. Modern bows with carbon arrows and good broadheads penetrate deep (complete pass-throughs on medium sized game are normal now) and cut vitals efficiently instead of crushing them like bullets do. The broadheads are as sharp as scalpels. I actually cut myself with a broadhead some years ago out in the woods. I didn't realize I had been cut until I noticed my glove was awful sticky, removed it, and found I had sliced myself quite nicely. I was able to wring blood out of my glove and I never felt a thing.
There's nothing inhumane about using a bow as a hunting weapon.
Killing an animal with a bow requires being close to that animal...generally 30 yards an in. Getting that close usually means getting the wind just right in your favor, using the features of the land to your advantage, etc. Anyone who thinks its easy should go try it against white tail sometime. I've been skunked far more often than I've been successful.
Hunting is not an equal initiative endeavor. The critter you are hunting is going to be busy looking for food or looking for a mate when you interrupt its day with death. If it knows you are there, you don't bag the animal. So you intend to ambush it. Same thing that the lion does to the gazelle. Same thing that the meat processor does to the cow that was on your grill on July 4th. You know, the holiday where it's tradition to gather together with friends and family and share meat from a critter that frankly didn't really need to die to keep anyone from starving? Everybody enjoyed the dead critter and I dare say nobody felt bad about it.
Unfortunately the cow people ate a couple of weeks ago didn't have a PR campaign.
If the animal was taken legally, there's no foul. If it was taken illegally, there are resources to prosecute the person who did it made possible in large part by the fees paid by people who DO sport hunt legally.
This whole thing is absurd.