A friend was wondering why Cole would be afraid of becoming a despair demon, as opposed to a spirit of, say, cruelty. He did not see the connection between compassion and despair.
It seems to me that when a spirit becomes corrupted, it does not become its opposite. Rather, it twists into a darker version of itself, one that takes things too far. For example, Justice becomes Vengeance, rather than injustice. Wisdom becomes Pride, not foolishness.
Compassion sees all the pain in the world, and seeks to help. Corrupted, Despair sees the same pain and gives in, hopeless. In this light, it is quite easy to see how Cole became a murderer in Asunder.