Because the reason we are given is not "the deer was going to die anyway, killed by either the Amazons or the boar, because both hunters needed its meat; but the Amazons were going to kill it quickly and painlessly, so they might as well be the ones to do the killing instead of the boar".
The reason we are given, as stated in the text, is "the boar was going to kill the deer painfully, so the goddess sent the Amazons to prevent that by granting the deer a quick and painless death before the boar could prey on it."
Notice that Polly never tells Diana "you don't want to kill it? What, do you think the meat you have been eating all your life didn't come from dead animals?", she just makes it a matter of sparing the deer a painful death. Diana is enraged when the boar kills the deer, and the boar's death is later portrayed as "poetic justice", despite the fact that the boar really did the same thing all hunters, Amazons included, do: kill their food; the only reasons boars don't kill their preys painlessly is because they don't happen to have arrows to strike directly at the heart.
So the head-banging is because hunt is not portrayed as "carnivores and omnivores kill herbivores in order to eat their meat and survive, and different predators compete for their preys"; it's portrayed as "evil animals prey on kind animals, and the Amazons try to prevent that, and then avenge the poor kind animal, because they are noble and just."