> There's nothing wrong with giving your own species a higher moral weight.

Without reason, I'd say there absolutely is something wrong with that. In fact, I'd argue there's no such thing as "human morality", only morality, which applies to humans (and other species). There are certainly some applications of moral law that only apply to humans, but that also applies to other species as well. Again, there's no rightful pedestal to put humans on.

> It derives quite naturally from us being the result of self-interested genes.

You're making an implicitly claim here that what results naturally from our DNA is morally right. You'll have plenty of people arguing that as well.

Everybody treats different categories of living things differently. Most of us would save ourselves before a stranger. We prefer family to non-family, our in-group to our out-group, human life to non-human life, and dog or cat life to rat or cockroach life.

You can argue that all of these different categories have inherent moral worth and that moral worth is not dependent on the perspective of the person making the judgement about moral worth, but almost nobody actually behaves that way. And I would argue that the people who do behave that way are mostly confused.