Theists: What is the most compelling argument you have heard for Atheism?

[masterofpuppets]

That's like asking how the lottery winner knew to choose just those numbers.  We're living in the 'winning ticket' and are part and parcel of it.

The lottery is not a good analogy for the fine-tuning argument. A better analogy is if there were billions and billions of white ping pong balls and one black ball. If the black ball rolls down the shoot, you can live. A white one, you will be shot. Each individual white ball is equally improbable, but the odds of you getting some white one is overwhelming. Now, to get closer to the actual odds, you would need to see that black ball roll down the shoot 5 times in 5 drawings in a row to live. If you witnessed that happening, you would be certain that the game was rigged. So we are not interested in why you got the particular ball you did (ever ball was equally improbable), but why you got 5 life-permitting balls in a row. 

That, in a nutshell, is the fine-tuning argument. We are not interested in why this universe exists, but why a life-permitting one exists. As in the drawing above, we have very good reasons to think the universe was rigged for life.

If the physical constants were different, life as we know it might not exist. It doesn't follow that life couldn't exist.

Even the assertion that "our universe is life-permitting" is quite misleading. The fact that we haven't observed any life outside of Earth, even with an abundance of Earth-like planets out there, is good evidence that our Universe is barely life-permitting at all (that is to say, almost not life-permitting). Life just managed to precariously evolve on one tiny planet in the Milky Way.