The Selfish Gene does not refer to a gene that makes us selfish. It does not in any way seek to carry a moral connotation that we are inherently selfish (though that may be true).
The emphasis is on the second word.
The point of the selfish gene is that it is the gene that is trying to replicate, trying to see its descendants in future generations, trying to out-compete its fellows. In this view individual creatures are just bundles of genes from an evolutionary point of view. We are vehicles for the real actors. The competition at the creature level is just a manifestation of the competition among genes. This approach is why creatures cooperate with their family members more than other individuals: because they share more genes.
So can we not use “selfish gene” as if it was a scientific doctrine of original sin?