During the time of slavery owning slaves meant power. As people gained slaves and thus gained power they became greedy and would do whatever needed to remain in power. Power seems to lead to corruption.
There can be many answers to this question. The most evident of them would be that the ownership of another human being ends up creating and enhancing a dialectic between two people that is predicated upon domination and submission. It is this dynamic that ends up becoming corrupting and corrosive to the bonds between human beings and the sensibilities and promises of any great democracy. I would cite Frederick Douglass' narrative as an example of this. The case of Sophia Auld would be one such example. At the start of her interactions with Douglass the slave, she is benevolent, even teaching him to read and write. Yet, when admonished by her husband about how there has to be a level of control over slaves and that deviating from this carries with it a tendency of abuse, she becomes cold and no different than any other slave owner in her treatment of Douglass. In this light, slavery corrupts those who are in control as they are no longer able to treat others with dignity, and as ends in of themselves. Instead, they can only abuse and dominate through repressive means as they treat individuals as means to ends.
Many people argued that slavery was bad for both the slaves and the slaveowners. The idea here was that it made the slaveowners into tyrants.
If you think about it, no one in a democratic society has (or is supposed to have) absolute power over anyone else. We believe that power corrupts and, as they say, absolute power corrupts absolutely. This is what happened (some say) to slaveowners. Basically, owning slaves let these people do what ever they wanted to other people. It encouraged them to think only of themselves and to use other people as tools to get what they wanted. (This is also something we try to teach against on a personal level -- we tell our kids not to be selfish, for example.)
Think, for example, about the impact that slavery seems to have had on the sexual morality of some male slaveowners. They had a captive bunch of women who could not refuse to sleep with them. This corrupted them and made them forget the idea of fidelity to their wives or of trying to control their desires.
Owning slaves, then, corrupted people by letting the forget about controlling themselves and by allowing them to do whatever they wanted with respect to their slaves.
Slave owners felt superior. Having power over a person can change who a person is. When they have slaves they have this ego and slowly they become more and more inhuman towards slaves because they feel like they owe them nothing. This mindset could be like poison.