You may be right that some form of reciprocal altruism is necessary to the development of social animals. However even this would be an empirical claim, that whilst having a strong correlation to the natural world is itself arbitrary.

Why? Because if the planet was a little bit warmer or a little bit colder, maybe we would more efficient food resources which would have allowed more energy to be directed to the brain, and maybe we could have (we might still) develop a form of telepathy whereby it would be impossible to lie and cheat and reciprocal altruism would not be required.

This is an undoubtedly convoluted example, but I think the point is that our behaviour is entailed by organic and alterable processes and not some objective schema.

I think you’re right to suggest that human morality is based upon a cultural evolution that allows reasoning and higher cognitive functions. We don’t just emotionally react to everything we come into contact with. If I had more room in the essay I would’ve talked the false dichotomy between Hume and Kant, they both want to hold onto one end of the spectrum of the reason / desire split to the exclusion of the other.

I explore this a little in Subjectivism: Some problems

I think the evolutionary moral impulses may be less arbitrary than you imply (of course I agree they are not a source of objective truths). It may be that most or all social animals would share many of the same impulses, and further, it may be that being a social animal was a key ingredient to achieving a high intelligence.

In any case, your take on Hume and Kant is interesting and your concluding sections make good points. I would more explicitly add that it is cultural evolution which provides an engine for further phases of moral development which integrate the moral impulses from physical evolution with our further reasoning about such issues derived from our higher cognitive skills.