But some people think that the Bible allows or even commands us to keep slaves. If that's the case that seems to mean that God of the Bible is less than perfect morally. Fortunately for us, God, Jesus, and the Bible do not allow keeping slaves. So there's your short answer.
How about a slightly longer answer? Try these:
"There is neither Jew nor Gentile, neither slave nor free, nor is there male and female, for you are all one in Christ Jesus." Galatians 3:28In Jesus' ideal world, all people are equally important. If everyone is meant to be equal, then slaves are a complete no-no.
"For we were all baptised by one Spirit so as to form one body--whether Jews or Gentiles, slave or free--and we were all given the one Spirit to drink." 1 Corinthians 12:13Just to reiterate a point...
And finally, in case so far it sounds like the New Testament is OK with slavery because one day slaves won't exist any more, here's an Old Testament verse to put it all in perspective:
"Anyone who kidnaps and sells another person must be put to death. If they still have the person with them when they are caught, they must be put to death." Exodus 21:16The trouble I think most people have with seeing passages in the Bible about slavery is that they read them through 21st century eyes. For most of us, our understanding of slavery is completely based on the image of black people being taken from their homes in Africa and forced into hard labour by rich white people. They were seen as property, no better than livestock, and had no respect or rights. They were considered sub-human. When we hear the word 'slave', we think of the worst type of slavery, because that's what we're familiar with. We can call this kind of slavery 'chattel slavery'. Sounds a bit like cattle, if it helps you remember. (The word 'chattel' is derived from 'cattle' anyway).
But the above verse from Exodus clearly says that taking someone and holding them as property to be sold is wrong. If that doesn't describe slavery as we know it, I don't know what does.