I'm afraid you've misunderstood me again--I usually leave the webs in and around my house, I appreciate their beauty and their utility. I am not a hunter of spiders, for sport or otherwise. I offered the example only to show how in some contexts I might destroy something even though I appreciate it.

I believe we may each be using the word "appreciate" with subtly different definitions. I believe it's possible to appreciate aspects of a thing without necessarily collapsing them all into some sort of comparison of perceived total value. I think it's possible that someone who hunts for sustenance might also come to treat the activity as somewhat of a sport, or an art, and so come to appreciate aspects of the activity including the intelligent behaviours of the prey.

No I have not misunderstood you, maybe I haven't made myself clear enough(not a native English speaker here...). As you also say, the context itself is what matters. For example, today I would guess most e.g. Canadians do not hunt for survival. Having a Canadian hunter saying "I hunt elks for sports, but I appreciate them", is kind of funny and meaningless. In the context of hunting for sports, it is pointless to say "but I appreciate them". If you beat up your neighbor cause he attacked you with an axe, and you needed to save your life, it is pointless to say that you appreciate him. It is clear you did what you did, cause you appreciate your own existence more than him. It is equally pointless to say "but I appreciate him" after making clear that you beat him up, cause you din't like his face. In both cases, the context is clear and thus the level of appreciation to the other party. Stating "but..." is meaningless. That for, my understanding of what the level of appreciation of someone hunting for sports towards his pray, is that it is very low by my standards.