Even if we allow those false dichotomies to stand, the argument would still founder on the conclusion that evil "doesn't exist" because, we're told, evil is simply a term we use to describe "the absence of God's presence in our hearts." It doesn't follow.
The case, such as it is, has been built on the unpacking of purported opposites — heat vs. cold, light vs. dark. What's the opposite of evil? Good. To keep the argument consistent, the conclusion therefore ought to be: Evil doesn't exist because it's only a term we use to describe the absence of good.
You may wish to claim that good is the presence of God in men's hearts, but in that case you'll have launched a whole new debate, not finished one.
Albeit thoroughly butchered in the above instance, the argument as a whole is a classic example of what's known in Christian apologetics as a theodicy — a defense of the proposition that God can be understood to be all-good and all-powerful despite having created a world in which evil exists. This particular form of theodicy, based on the idea that evil is to good as darkness is to light (the former, in each case, supposedly being reducible to the absence of the latter), is usually credited to Augustine of Hippo, who first laid out the argument some 1600 years ago. God didn't create evil, Augustine concluded; evil enters the world — which is to say, good departs from it — via man's free will.
Augustine's theodicy opens up an even bigger can of philosophical worms — the problem of free will vs. determinism — but we needn't go there. Suffice it to say that even if one finds the free will loophole persuasive, it doesn't prove that God exists. It only proves that the existence of evil isn't inconsistent with the existence of an omnipotent, omnibenevolent deity.
Einstein and religion
From everything we know about Albert Einstein, all this scholastic navel gazing would have bored him to tears. As a theoretical physicist he found the order and complexity of the universe awe-inspiring enough to call the experience "religious." As a sensitive human being he took a profound interest in questions of morality. But none of this, to him, pointed in the direction of a supreme being.
"It does not lead us to take the step of fashioning a god-like being in our own image," he explained when asked about the religious implications of relativity. "For this reason, people of our type see in morality a purely human matter, albeit the most important in the human sphere."
Sources and further reading:
Einstein Letter on God Sells for $104,000
New York Times, 17 May 2008
Einstein on Prayer; Purpose in Nature; Meaning of Life; etc.
Atheist Professor vs. Christian Student
Newsgroup posting, 25 March 1999
The Problem of Evil
Last updated: 07/30/11