Good point. I think the fallacy of the atheist argument in question becomes even more apparent when written out in formal logic. Basically, the argument goes like this:

1. By definition, God is all loving so He would never desire evil to happen to anyone.
2. By definition, God is all powerful, so He is always able to bring about what He desires.
3. Evil happens to people.
4. Therefore, God must either be unable to prevent evil from happening to people or unwilling to prevent it.
5. If God is unable to prevent it then He is not all powerful, so He is not God.
6. If God is unwilling to prevent evil then He is not all loving, so He is not God.
7. Either way God, as defined as an all-powerful, all-loving Being, must not exist.
   Thus, the crux of the argument is that if evil things happen to people, then God must not exist. However, herein lies the problem: how does the atheist distinguish between good and evil? Everyone has some idea of what is good and what is evil, but different people may disagree about whether certain things are good or evil, so in order to objectively prove that evil exists, we need an objective way to distinguish between good and evil. From a theistic perspective, the obvious solution is to say that God is good by definition - God's character is what furnishes the objective definition of goodness and love. Evil, then, is simply defined as the antithesis of good, and so it is the nature of God that furnishes a means of objectively distinguishing between good and evil. Yet, if God does not exist, then neither does the distinction between good and evil. Thus, if the conclusion log the argument (7) is true, then the premise that evil exists (3) becomes false, and so the argument is anti-circular. Instead of the conclusion proving its own premises as in a circular argument, the conclusion disproves its own premises.