Humans are great. Humans are created by God as the pinnacle of his creative work and they, only they, are endowed with the ability to choose, agency. Also, with that comes the ability and apparently inclination to remove that agency from others.
Slavery is an ideology so radically opposed to humanism that it seems unbelievable that both could have coexisted at the same time. But coexist they did, for many decades even. The Atlantic slave trade went from the 16th to the 19th century, but the ideas of humanists such as Pico della Mirandola and Petrarch had already been around for years before the practice even started. How is it that this happened?
In considering Shakespeare's work The Tempest, I believe that one of the most important points was that if you do not consider someone human, then suddenly you can justify any treatment of them. After all, even women did not receive the same kind of adulation and praise as men did in the first days of humanism. Take Caliban, for instance. As a foreigner and a native whose first tongue is not English and whose customs are unfamiliar, it is very easy for Trinculo to ask "What have we here? A man, or a fish?...A fish: he smells like a fish, a very ancient and fish-like smell...". He even debates on how he could exploit this strange creature for money in England. This mirrors the reactions of many European settlers upon meeting native peoples. By not considering them as humans in the same sense as Europeans, the arguments of equal rights and privileges for all humans are no longer important.
Furthermore, the humanism of these times was what the American Humanist Association would describe as Renaissance Humanism, or "the spirit of learning that developed at the end of the middle ages with the revival of classical letters and a renewed confidence in the ability of human beings to determine for themselves truth and falsehood." This does not consider so carefully the distinction between church and state as later humanism would. Therefore, the religious precedents for slavery found in the Bible would seem a perfectly good excuse to the almost entirely Christian inhabitants of Europe.
Although on the face of it, this matter seems convoluted, it may not be a confusing as it seems. The world was just emerging from a feudalistic time where even those of the same nationality and race were practically enslaving each other in serfdom; why is it so surprising that rulers of the Renaissance would do the same to foreign groups? Humanism had a long way to go before it helped to abolish slavery in the 18th and 19th centuries.
Edwards, Fred. What is Humanism? American Humanist Association. americanhumanist.org. 2008. Web. 9 Sep, 2015.
Shakespeare, William (2014-09-25). The Tempest: Third Series (Arden Shakespeare) (Kindle Locations 4241-4242). Bloomsbury Publishing. Kindle Edition.