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

[SteveII]

And just how did they get just those highly exact inherent properties that so conveniently arrange themselves and why must the various trajectories be preserved according to very precise principles? Mere coincidence? They just do for no reason at all?

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.