Whereas the Creationists study the effects of Positive Energy, the Abolishers study Negative Energy.  Similar to how Positive Energy grows and strengthens what it touches, Negative Energy destroys and weakens what it touches.  It can be seen as sickness and disease in living things, and as deterioration and darkness in inanimate things.  Like Creationists, Abolishers seek to learn the secrets of Negative Energy, and how it can be harnessed and controlled.  It must be noted, that while the effects of Negative Energy are often associated with things that are "evil", Abolishers are not any more or less evil than any other Wizard.