This is so incredibly late it's ridiculous, but I just wanted to toss my hat in the ring:
I'm reminded of drug interactions, where medications can react oddly with each other, producing effects you wouldn't see in them individually.
The Cheetah-spirit is devoted to death and rage.
Anti-Life is very similar, but not identical.
The conflicting influences produced a reaction in Barbara's psyche that's radically different from what either of them would have done to her individually.