I said personhood, not humanity is unnatural among animals. A small number of species besides humans may count as close enough to people to be thought of as similarly anomalous. (Personhood is an anomaly within an anomaly, since life in general is unnatural in the context of the universe, as Schrodinger pointed out in What is Life? Organic processes run counter to entropy.)
There’s nothing anthropocentric about saying that personhood is unnatural, since that’s not the same as saying personhood is central or of ultimate importance. On the contrary, the implication is that people are alienated from the wilderness, which is why we busy ourselves with creating an alternative, self-centered, more ideal landscape for us to inhabit; we call it civilization (or living in our heads or in our worldviews).
Yes, morality consists of a code of conduct, a set of rules about what should and shouldn’t be done. The rules hold even if they’re not obeyed, which means that when we conceive of those rules, we’re not thinking of actual norms; we’re picking out certain behaviours as preferable, assigning them that value as given by an ideal, by a conception of a more perfect world, such as of the kingdom of God or Heaven (Tian in Confucianism and Daoism, or the Good in Platonism).
Sometimes, the moral rules are almost counterfactual in that they run up against normal human behaviour. That was the point of Jesus’s declaration that the first would be last and the last would be first. In short, his standards were exceptionally high, even fantastic (unnatural).
The idea was to bring Heaven to Earth. In secular societies, Heaven is replaced by a conception of Utopia, from the early scientistic conceptions to the corporate ones envisioned in advertisements and the sentimental ones pictured in Hollywood movies.
Those five moral proscriptions are certainly not normal in most animal species. Animals often steal, rape, trick each other, and kill. Animals give off false signals if doing so is advantageous to them, although the Handicap principle sometimes imposes a penalty for communicating, so the animal has to think hard about whether sending the signal is worth it. Alpha males sometime eat their rivals’ offspring, to avoid competition. Social animals prefer not to kill each other, since they survive better in the group; thus, they evolved elaborate nonlethal contests to settle their disputes. Likewise, most animal species don’t wage war (although some ants and chimpanzees do).
Our species is by far the deadliest (leaving aside viruses, bacteria, and insects). Our behaviour is often self-destructive, which is a sign of our greater degree of self-control (autonomy), which in turn is the basis of our moral evaluation. There’s no sense in speaking of moral properties outside of a context of freewill. That’s why the talk of moral rightness or goodness throughout nature is metaphorical at best and arbitrary at worst. Aristotle’s teleology is based on a comparison of natural causality with human artificiality (intelligently-designed functions).