Whatever he can get away with.
Anyone who prides them self on taking positions based purely on logic should be able to lay out the logic of their position on this very basic question about our form of government. Where are our rights derived?
Laws of men are only capable of taking rights. They are unable to give them.
Atheism is not a neutral position. Even someone who believes in a pixie creator will have a logical basis for their rights within our form of government. An atheist must rely on the good will of his fellow citizens. Trust me. Most of us not that nice.
Any of the other atheists around here wanna take on this challenge, I'll be around later.
Well, if you don't allow for the idea that our rights come from other men, then it's clear that nobody will be able to refute your argument.
You have succinctly summarized the fashion in which rights are purely illusory. Belief does not alter reality. If the atheist is wrong, they still have the rights granted by God. Gravity does not disappear if you disbelieve in it.
What you have done is provide evidence for the fact that "rights" in the immutable sense do not exist. People assert them in the same way a child asserts Santa Claus -- those assertions determine no objective reality on their own. If such rights were an objective reality, they could not be routinely violated.
One can only come to the conclusion that it does not matter where one asserts rights come from (of if they exist at all), because the reality is the same regardless. Relying solely on the arbitrary (and probably false) belief of your neighbor for good will is a flimsy protection at best. Fortunately, the motivation for being a decent person is the same as it always has been regardless of belief: it is to the long term benefit of the individual to be a good neighbor, and those that are decent prosper. Prosperity and happiness is all the motivation most people need. For everyone else, no belief is going to keep them out of trouble for long.
I would make the tangential observation that most of the atheists I know, and I know many living where I live, are conservatives. The belief that compels them to be conservative is that conservatism is rational, and little more. Everything else follows.
It's very simple, "god-given rights" is replaced with "natural rights." It's the concept that rights aren't given by God, but that we, simply by virtue of being human, have certain rights that can't be taken away. Natural rights are derived from natural law, which in general encompasses both the concept of "god-given rights" and "natural rights."