First, people have already heard the arguments against the practice. The case against slavery didn't emerge in a blinding moment of moral clarity, for instance; it had been around for centuries.
Second, defenders of the custom tend not to offer moral counterarguments but instead invoke tradition, human nature or necessity. (As in, "We've always had slaves, and how could we grow cotton without them?")
And third, supporters engage in what one might call strategic ignorance, avoiding truths that might force them to face the evils in which they're complicit. Those who ate the sugar or wore the cotton that the slaves grew simply didn't think about what made those goods possible.