Take this passage from Steven Pinker:
The child sees things differently. Though an offspring has an interest in its siblings' welfare, since it shares half its genes with each full sib, it shares all of its genes with itself, so it has a disproportionate interest in its own welfare (The Better Angels of Our Nature p.431).A child typically having greater interest in its own welfare than that of its siblings has nothing to do with its genes. It has to do with being a motivated being which experiences its own existence rather more intensely than it does other people's.
It is likely that a child will have greater empathy with its siblings than with other folk, but that is to do with long and intimate association. Nor does that always work out: siblings can end up disliking or even hating each other. Moreover, the capacity to see others as "sibs" is a moveable feast, that can be adopted by other social mechanisms. The whole notion of "brothers in arms" works on that. Similarly, it is a much-attested feature of life on a kibbutz that those raised together because quasi-siblings, if even if there are no common genes.
Yes, natural selection works to select for certain behavioural traits. Such as the capacity to develop strong, non-sexual (or even de-sexualised) attachments to others. But the genes themselves do not provide any sort of motivation: they do not drive behaviour in that sense. Hence a capacity that evolved for one reason can end up being attached to other behaviour.
The real power of natural selection is to see how order can evolve without intention. Putting intention "back in" misses the explanatory power of natural selection, not to mention committing one to false characterisations of human behaviour. Writing in such intentional terms does not display your understanding of natural selection, it displays a serious lack in such understanding.
(BTW This is not a shot at Pinker or his book: which is a great and enlightening read. He just provided an example of an all-too-common mode of thinking about natural selection.)
ADDENDA Further on, Pinker adds the caveat:
As always, teleological terms in the explanation--"wants," "interests," "for"--don't refer to literal desires in the minds of people but are shorthand for the evolutionary pressures that shaped those minds (p.431).But the notion that framing language in intentional terms has no implications is naive at best. Shaping capacities is very different from motivating actions, as we can see from considering how the capacity for non-sexualised/de-sexualised attachment can operate for non-relatives. The language of intention is certainly easy and familiar: it is also highly misleading.