As you note . . . “because God says it is wrong” IS what is different. Without God there is no rational basis for altruism.
Not at all. Altruism is a predictable result when dealing with species that live in tight social groups. In these situations genes favoring altruism spread rapidly because sacrifice on the part of one person carrying an altruistic gene in order to preserve several other people (most likely related and also carrying these altruistic genes) amplifies their frequency over that of selfish genes. For example, one altruistic man may sacrifice himself to save his three children, two of whom carry the same altruistic gene. On the other hand, another man without an altruistic gene would allow his children to be killed, thus leaving one selfish gene in the population while two altruistic genes are preserved. This is the process called kin selection, and this principle has been found to have predictive power in the behavior of organisms ranging from plants to people to insects.
Kin selection probably initially favored only offspring, and was so useful that it then extended to other kin. Humans now have such an instinct for compassion that we extend altruism to even members of other species.
That is why we feel like being altruistic, why I think we ought to is another reason. I think the basis for morality is every person's feeling about how they individually should be treated. Everyone believes he or she ought to be treated well. Then rationally we know that no person is inherently more valuable than another, so by extent we should treat others as we would like to be treated. I do not want others to steal from me and I am no more special than any other human, so I should also not want others to be victims of theft. That is the rational basis.
Stalemate.