The theory is that God must not exist because He allows evil to exist.

Yes or no:
    Does evil exist in the world?
Yes or no:
    Does good exist in the world?

Are you in heaven right now?
Are you in hell right now?
Are we in a place right now where both good and evil exist side by side?
Is it possible there may be a time coming when good is separated from evil?
Are we merely pawns on the battlefield of good and evil?

From the atheist's side, the theory is based on questions, not answers. Lacking any evidence and resorting to just a theory punctuated by questions, the atheists argument does not provide a compelling reason other than assumptions founded in a faith of the absence of God.

From the Bibles' side, it is clearly articulated that good and evil both exist. Actually rather than relying on questions to make a point, the Bible provides answers to those very questions.

If an atheist asked "How could a God exist that allows evil to exist?" a theologian might reply with something like... "Because you aren't in heaven. You are on earth where the devil is competing for power. And furthermore you won't be free of evil until you get to heaven".