I don't think it was veiwed as immoral during the day. They cite the bible which even in the Ten Commandments mentions Servants (slaves). So I can't say but your veiw of morality that it is immoral.
Now, with that as it is, Yes Slavery is and was wrong. But if morailty does not change then who am I to say Abraham father of Isreal, was an immoral man?
Mary Chestnutt seems to have written, or admitted that she knew the practice of slavery was morally wrong and brought down judgment on the South.
Just because something appears in the Bible doesn't make it morally right. Abraham and Sarah sinned when they didn't trust God to fulfill his promise to them. They took matters in their own hands and the world has been paying for it ever since. Same story Adam and Eve.
Besides, the Biblical notion of slavery was different than the Southern variety. Onesimus, for example, and others were indentured for a certain time period and could even sell themselves back into slavery when their time was up.