You cannot prove that God doesn't exist; therefore, atheism is based on faith.
Often theists will try to place atheism and theism on the same plane by arguing that while theists cannot prove that god exists, atheists also cannot prove that god does not exist. This is used as a basis for arguing that there is no objective means for determining which is preferable because neither has a logical or empirical advantage over the other. Thus, the only reason for going with one or the other is faith and then, presumably, the theist will argue that their faith is somehow better than the atheist's faith.
This claim relies upon the erroneous assumption that all propositions are created equal and, because some cannot be conclusively proven, then therefore none can be conclusively disproven. So, it is argued, the proposition "God exists" cannot be disproven.
But not all propositions are created equal. It is true that some cannot be disproven - for example, the claim "a black swan exists" cannot be disproven. To do so would require examining every spot in the universe to make sure that such a swan did not exist, and that simply isn't possible.
Other propositions, however, can be disproven - and conclusively. There are two ways to do this. The first is to see if the proposition leads to a logical contradiction; if so, then the proposition must be false. Examples of this would be "a married bachelor exists" or "a square circle exists." Both of these propositions entail logical contradictions - pointing this out is the same as disproving them.
If someone claims the existence of a god, the existence of which entails logical contradictions, then that god can be disproven the same way. Many atheological arguments do exactly that - for example they argue that an omnipotent and omniscient god cannot exist because those qualities lead to logical contradictions.
The second way to disprove a proposition is a bit more complicated. Consider the following two propositions:
1. Our solar system has a tenth planet.
2. Our solar system has a tenth planet with a mass of X and an orbit of Y.
Both propositions can be proven, but there is a difference when it comes to disproving them. The first could be disproven if someone were to examine all of the space between the sun and the outer limits of our solar system and found no new planets - but such a process is beyond our technology. So, for all practical purposes, it is not disprovable.
The second proposition, however, is disprovable with current technology. Knowing the specific information of mass and orbit, we can devise tests to determine if such an object exists - in other words, the claim is testable. If the tests repeatedly fail, then we can reasonably conclude that the object does not exist. For all intents and purposes, the proposition it disproven. This would not mean that no tenth planet exists. Instead, it means that this particular tenth planet, with this mass and this orbit, does not exist.
Similarly, when a god is defined adequately, it may be possible to construct empirical or logical tests to see if it exists. We can look, for example, at the expected effects which such a god might have on nature or humanity. If we fail to find those effects, then a god with that set of characteristics does not exist. Some other god with some other set of characteristics may exist, but this one has been disproven.
One example of this would be the Argument from Evil, an atheological argument which proposes to prove that an omniscient, omnipotent and omnibenevolent god cannot exist alongside a world like ours which has so much evil in it. If successful, such an argument would not disprove the existence of some other god; it would instead merely disprove the existence of any gods with a particular set of characteristics.
Obviously disproving a god requires an adequate description of what it is and what characteristics it has in order to determine either if there is a logical contradiction or if any testable implications hold true. Without a substantive explanation of just what this god is, how can there be a substantive claim that this god is? In order to reasonably claim that this god matters, the believer must have substantive information regarding its nature and characteristics; otherwise, there is no reason for anyone to care.
Claiming that atheists "cannot prove that God does not exist" often relies upon the misunderstanding that atheists claim "God does not exist" and should prove this. In reality, atheists merely fail to accept the theists' claim "God exists" and, hence, the initial burden of proof lies with the believer. If the believer is unable to provide good reason to accept the existence of their god, it is unreasonable to expect the atheist to construct a disproof of it - or even care much about the claim in the first place.