When people say that there is no god, what they mean is that there is no Yahweh, the christian god. This shouldn’t be such a hot-button issue, but it is because a lot of people feel very strongly about it. It clouds their judgment and makes it hard to talk to people about.
Atheists don’t just not believe in Yahweh. We don’t believe in any other gods either, and christians forget that. They forget that Zeus is a god, and both groups don’t believe in him. The difference, of course, is that christians believe he doesn’t exist, and atheists either believe that he doesn’t exist or don’t believe that he does exist. There is a difference, and the difference is certainty. Christians are sure that Zeus doesn’t exist because they are sure that Yahweh exists even though there is no evidence for either. Gnostic atheists are equally sure of the nonexistence of any god, and agnostic atheists are equally uncertain about the existence of any god. We’re open to evidence. We just haven’t been shown any.
Christians think that by referring to their god as God, it makes him special. It doesn’t. He’s just one of millions of gods dreamed up by people over the hundreds of thousands of years we’ve been on this planet. I can’t prove that he doesn’t exist, but I don’t have to. Evidence of a thing’s nonexistence isn’t necessary for belief in that thing to be absent. My beliefs are based on evidence and logic. If something cannot be proven, then it should not be believed. That is the essence of my atheism.