Provide a convincing argument against slavery that would be convincing to anyone who thinks slavery isn't wrong, without any explicit or implicit theological appeals.
I actually think that, at least for long periods of history, the institution of slavery is defensible from the standpoint of utilitarianism, for example. It is now a socially unpopular idea. But so is infanticide and bestiality, but Peter Singer is prepared to defend both.
I don't think it can be done. It's a dog eat dog world, only the fittest survive, if we have the power to enslave others, what's wrong with it? It will certainly help me pass on my genes. Owning slaves gives people a selective advantage.
Believe, me I despise slavery. But I don't see a universally convincing secular argument.