Why does something exist rather than nothing? There are two categories of things which exist: those which exist necessarily (those things which don't depend on a certain set of circumstances to exist, but rather must exist) and those which exist contingently (those things which don't have to exist, and must have been caused by something outside of them). In this debate, we will be focusing on why the universe exists instead of not existing. It must have an explanation for itself-- either it necessarily exists, or something else caused it.
A way of reasoning through the question of the universe's explanation is a form of the Leibnizian cosmological argument from contingency:
"1) Anything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause. 2) If the universe has an explanation of its existence, that explanation is God. 3) The universe exists. 4) Therefore, the universe has an explanation of its existence. (from 1, 3) 5) Therefore, the explanation of the existence of the universe is God. (from 2, 4)"
This argument points out that everything has an explanation for its existence, either in its necessity or in being caused. As a result, something which is contingent requires that it is grounded by something which is necessary. If the universe is contingent it requires a necessary cause. According to Leibniz, this necessary cause could only be God.
The other alternative is that the universe is necessary. However, big bang cosmology has shown us that the universe began to exist at a finite point in time, which suggests that it could have not come into existence at all. In other words, it does not have to exist. Furthermore, if the universe is said to be necessary, what could this mean? Does it mean that every single quark which composes all of the matter in the universe is necessary? There could be no more or less? This seems absurd.
It is obvious that since the universe began to exist and could have not come into existence at all, it is contingent. All contingent things require a cause, and must ultimately go back to a necessary cause-- something which must exist because of its nature. Otherwise, things would simply pop into existence out of nothing without a cause. As the kalam cosmological argument puts it:
A. Anything which begins to exist has a cause.
B. The universe began to exist.
Thus, the universe has a cause.
While some atheists may counter Leibniz's assertion that the only explanation for the universe would be God by saying that this universe may have simply emerged out of another, this doesn't solve their problem. If what caused the universe is also material and thus contingent, then THAT would necessarily require a transcendent cause, or else the atheist is faced with having an infinite regress. As philosopher William Lane Craig argued, paraphrasing Liebniz in his book Reasonable Faith:
"imagine that a series of geometry books has been copied from eternity; such an infinite regress would still not explain why such books exist at all. But the same is true with regard to past states of the world: even should these be infinite; we have yet to discover a sufficient reason for the existence of an eternal universe. Therefore, the reason for the universe's existence must be found outside the universe, in a being whose sufficient reason is self-contained; it is its own sufficient reason for existing and is the reason the universe exists as well. This Sufficient Reason of all things is God, whose own existence is to be explained only by reference to Himself. That is to say, God is a metaphysically necessary being."
Since the universe consists of all space, time, and matter, that which caused it must be spaceless, timeless, and immaterial. This cause must also have a will capable of bringing the universe into existence, for although abstract things like numbers are spaceless, timeless, and immaterial, they stand in no causal relation to anything else and have no wills by which to bring anything about, let alone a complex, highly organized universe governed by strict laws and capable of producing highly developed life.
The only alternative for the atheist is to assert that the universe exists with NO explanation at all. For obvious reasons, he/she will not want to admit this. To do so is to make a mockery of logic and the obvious truth that everything which exists requires an explanation for its existence. After all, we do not genuinely worry that a giant sperm whale might simply appear in the earth’s atmosphere and land on our house (infinite improbability drive aside).
When asking why something exists rather than nothing, it's also important that we ask what kind of thing this "something" is. I have demonstrated that in the case of the universe, it is contingent and came into existence at a finite point in time, and so the explanation for it must then be God. However, I could go a step further and point to the obvious marks of design and fine-tuning in this universe, which further demonstrates that there must be a mind behind it. While I cannot claim any expertise in physics, I will take Stephen Hawking at his word when he says:
"The laws of science, as we know them at present, contain many fundamental numbers, like the size of the electric charge of the electron and the ratio of the masses of the proton and the electron... The remarkable fact is that the values of these numbers seem to have been very finely adjusted to make possible the development of life" (A Brief History of Time, p. 125).
Similarly, Dawkins admits in his book The God Delusion that, "one of the greatest challenges to the human intellect... has been to explain how the complex, improbable appearance of design in the universe arises," and that, "the natural temptation is to attribute the appearance of design to actual design itself" (p. 188 paperback edition). These atheistic scientists provide further corroboration for the premise that the “something” which exists exhibits hallmarks of design, and thus strengthens the argument that it was caused by an immaterial, timeless, causeless, spaceless intelligence.
So why does something exist rather than nothing? God exists because He must. He can’t do otherwise. The universe, which began to exist, exists because it was caused, and the only good candidate for the cause of the universe is God.