You're right that if someone asserts something, they should demonstrate why its true. The problem comes at this assumption you have that atheists are people who assert no god exists. When someone comes up to you and says "There is no god!" that's more then an atheists position even is. An atheist is someone who doesn't assert a god exists. It's someone who doesn't believe in a god. That's completely different then someone who asserts god doesn't exist, or someone who believes that gods don't exist. I have met an innumerable amount of atheists in my life, and yet I have not met one person EVER who believes god doesn't exist. That isn't to say that someone who would believe in no gods wouldn't be an atheist, it just is irrelevant to an atheists position. This is your mistake. You assume that an atheist believes in no god, which is wrong. Atheists just don't believe there is one. Anyone who can't tell the difference between those two things I hope is never a juror in a case of any significance. After all, they might think that because the preponderance of the evidence indicating someone is not guilty is somehow the same as the courts asserting that the person is innocent.
http://blog.minitab.com/blog/understand ... hypothesis
You're fighting a strawman position held by no one, then labeling that as some particular atheists position. It isn't.
However, if it is, your person there needs to demonstrate their wild claim that there is no god, like you said. They are still an atheist, but they are making a separate claim unrelated to atheism. Some sort of wacky counter-theistic claim, which isn't even named because nobody has it.
Granted I've had one or two head injuries in my lifetime, does this make any sense to anyone else?