"the claim that human life is *more valuable* than other animal life is rooted in the same thing that makes killing civilians/soldiers in other countries *less evil* than murdering someone in your own country."
Not *less evil*, honourable, glorious, and in general considered a good thing. Again because, as you say, evolutionary need to preserve your tribe.
However i'd go on describe this claim as an attempt to control your environment, to have confidence that other tribes are not a threat and affect how they behave such that your tribe, at worst, breaks even. (neutral or positive impact)
Animals on the other hand are useful as a source of food (meat, milk, eggs), raw materials (wool, animal skins, bone for tools) and labour (especially elephants, but also dogs). The use of animals is not limited to killing them for food/glory, it is about enhancing our own survival and using what will maximize our efficiency.
Intelligence and rationality may, infact, extend our protection to the ecology which supports us. It happens to be useful to control that environment in order to sustain ourselves. That is why i think we see a trend toward environmentalism and forcing corporate entities to pay for damage to societal resources like the sea, or biodiversity.
It is my ability to self-reflect which i use to consider what i should value, it allows me define what *should* be valued, and that in itself is valuable. However, it is not the ONLY thing which *should* be valued.