This isn't really my area, but I wanted to address this question and particularly I feel there is a misperception about slavery in Europe. Essentially slavery declined in Christian Europe, and was for the most part absent by the end of the middle ages. It then re-emerged due to colonialism, but was for the most part practised in the colonies, not in Europe itself. It was then abolished, at least in law, across most of Europe relatively early on. American slavery, while it needs to be read against the background of Europe, is not a good model for understanding the history of slavery in Europe (and I think this is what I react against - people who think slavery in the States was simply a continuation of 1700 years of slave-keeping in Europe).

There's three movements we need to consider in terms of your question. Firstly, what was the situation of slavery in European societies before the rise of Christendom; secondly, how did Christianity function to diminish and almost eliminate slavery throughout Europe. The third question is why did slavery re-emerge as a significant social practice around the time most often associated with, for instance, the trans-Atlantic slave trade.

We need to remember that slavery was part and parcel of the 1st century Roman world, and the idea that you could own a human being was philosophically well entrenched. This changed under Christianity which held as a basic tenet the equality of human beings before God, so much so that while it is a mistake to think of early Christianity as 'egalitarian', since it often maintained hierarchical patterns within society, it did create a notion of absolute value of human life and freedom. Arguably this lead, though slowly, to the decline of slavery across Europe. By the middle ages slavery in connection with Europe was mostly associated with the 'frontiers' of Christian Europe - areas with significant interaction with pagan or Islamic peoples. Partly this is because holding a fellow Christian as a slave was illegal whereas holding a non-co-religionist was in some places acceptable. At least in Europe, serfdom effectively replaced slavery as the means of tying people to land and to agricultural systems.

To see the re-establishment of slavery in Europe, you want to look at the rise of colonial and imperialist efforts from the mid 15th century. For example, the Papal Bulls Dum diversas and Romanus Pontifex legitimised Catholic slave-trading of non-Christians in relation to the colonial efforts of Portugal in Africa. However, you can see things go the other direction in Spain, so that Charles V outlaws slavery in the whole Spanish Empire in 1542 primarily on the advice of theologians and lawyers.

Likewise, while slave-trading was practised by the British, it took place in the African arena, and slavery itself was mainly confined to British Imperial territories, including the 13 colonies. From 1772 one could not actually be a 'slave' in mainland England, and so technically there was no slavery. Slavery was, for most European powers, a necessary and out-of-mind evil that allowed their colonial empires to flourish. Slave labour propped up imperial territories and provided the man-power for large scale agricultural enterprises in foreign territories, not domestic ones.

The main rationalisation for Christian Europe was based on two ideas. The first was that the state of humans was naturally free. This was, I would argue, one of the effects of Christianisation across European society. However it was tempered by a recognition that states and secular authority had the right to overrule, in this instance, natural law with secular law, for the purpose of order and social good. This provided a rationalisation for slavery. Furthermore, the status of non-Europeans and non-Christians meant that their treatment could be differentiated so that while enslaving Christians was a sin, the slavery of non-Christians was acceptable (but not necessarily theologically approved, there's an overlap here between what the Church deemed permissible and what society put into practice).