The question Who made God is commonly used to argue against the existence of the sort of god traditionally believed in by Christians, Jews, Muslims, and many other monotheists. Strictly speaking, this isnt an independent argument because it is not offered on its own. Instead, it is used as a rebuttal to the claim that our universe is too complex and intricate not to have been designed.
According to this common theological argument, nothing so complex as the universe with all of its accompanying natural laws could possibly have occurred simply due to random chance; ergo, it must have all been designed and created by some being which believers label god. This can only establish the existence of a creator god, but that is usually enough of a basis for many to then proceed with further arguments to show that a creator god must be the same god of their religion.
The response Who made God? can be used to point out an important flaw in the above argument: if the universe is too complex not to have been designed, then God is also too complex not to have been designed. A creator-god is never portrayed as something simple or, more importantly, something simpler than the universe. If this god is at least as complex as the universe, then it needs a designer and creator at least as much as the universe.
Believers will usually respond with one of a couple of common objections. The first is to claim that this creator-god has always existed while the universe has not; because the universe began to exist at some point, it requires a creator in a way that the god does not. Unfortunately, the assertion that this god always existed is unsupported and apparently unsupportable its just an assertion we have no particular reason to believe. The assertion that the universe began to exist is also problematic because time itself is a feature of the universe, and therefore the universe does not exist in time such that we can talk about a time before the universe or a time after the universe.
Another objection raised by believers is the idea that their god is a necessary being and doesnt need a creator. Unfortunately, this is also unsupported and unsupportable. There is no basis for such an arbitrary assertion, except to try to excuse their god from the same standards they wish to apply to the universe.
Moreover, both of the above excuses made for this god can be equally work for the universe. Why cant the universe be necessary or not need a creator? Why cant we say that the universe has always existed because there is no identifiable point in time when the universe did not exist? No one can say after all, we really dont know enough about our universe or universes in general to make such judgments. Of course, we also dont have enough verifiable data of gods to make such judgments about them, either.
Another possible objection, also ad hoc in nature because it is only brought up in order to explain away this argument, is the idea that the complexity being discussed only applies to material things. God, being immaterial, is not subject to the same standards. This objection falters, however, because the same people offering it also typically believe in immaterial souls, thus leading to the unorthodox belief of our souls existing in parallel with this god rather than being creations of this god. Although someone could hold such a belief, it isnt one you will likely encounter; as a result, it is unlikely that this objection can be used consistently or successfully with the persons beliefs.
The question Who made God? does not quite suffice to prove that the traditional God believed in by Jews, Christians, Muslims, and others does not exist. It does, however, manage to show that one of the most common and popular reasons used to support belief in such a god is highly problematic and probably cannot serve as rational grounds for belief.

