I'm not a hunter, so I won't criticize, but I like Eric's and Djr's thinking on this myself, and that's the sort of hunter I hope to become some day. It's a similar mindset to that of all the traditional hunters I've seen in documentaries, articles, books, etc., such as the Bushmen of southern and central Africa and the Chukchi of eastern Russia. Interestingly, the hunters of both these cultures, separated by thousands of miles and thousands of years, stroke a large animal after killing it and thank it for giving its life so that they and their children and tribe can live. I don't know if I'll necessarily do that, but I hope I'll maintain that sort of respect for the animal.
Traditional peoples tend to see prey animals as not just food, but as relatives with spirits. As equals or near-equals. It is only neolithic civilization that demeans animals into mere food products. For some reason, it baffles most vegans that traditional people would eat spiritual relatives like American bison, but it doesn't baffle the vegans that wolves would eat bison--even though the bison is more the wolf's equal than the human's. One comment that a Native American made was that modern people seem to think too much with their brains (such as when vegans say we shouldn't eat meat because we have brains enough to know it's wrong and unhealthy--both falsehoods) and not enough with their hearts/spirits.
One great evolutionary advantage to the traditional way of hunting and respecting animals is that it encourages tribes to only kill the minimum number of animals they need to survive and thrive. This probably became an important adaptation after Homo erectus and other proto-humans likely exterminated many of the megafauna and the megafauna started becoming relatively scarce (though no-where near as scarce as today--which is why we should be even more respectful and careful today, rather than less so).
