What is the difference in hunting dear with a rifle, bow or spear?
Very basically, 80 to 180 grains at 2,000 to 3,000 feet per second, vs 400 to 600 grains at 200 to 300 FPS vs the spear weight at 100 fps. I've no idea what kind of energy the spear develops, but my guess it would easily kill a deer. If they're an objection, I'll speculate that people consider it "barbaric".
The latter two weapons require more skill, and are more likely to allow the animal to escape wounded and die slowly. I have no problem with a skilled hunter using any weapon for a clean kill, but I have a problem with leaving a wounded animal to suffer.
I can't think of a good way to address this with regulation, but if I were going to bow hunt, I'd want to have a gun along to finish the job if necessary.