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

[Neo-Scholastic]

You seem disingenuous, so there's that.

By adding the qualifier 'seem', you also seem to be giving me the benefit of the doubt. I appreciate that.

Can you give an example of a universe that you would NOT consider fine-tuned?

A "Loony Tunes" world would not be fine-tuned. And the comic book universes of Marvel and DC have fairly arbitrary physical laws. The LEGO movie worlds are clearly fine-tuned but the mystery remains as to how modular blocks and pieces produce living conscious beings like Bat Man.

Nevertheless your point is well taken and that is why I am not a fan of the fine-tuning argument as commonly presented. To my mind, whether the physical constants are uniquely suited to life is not particularly important. To me the two important parts of the argument are: 1) the observation that the physical constants at least appear to be contingent (i.e. they could have been otherwise) and 2) the universe seems to manifest a rational order.

SteveII sets up three options (necessity, chance, and design) to explain why the universe appears contingent and rationally ordered. As for me, my posts have admittedly been dancing around my position rather than laying it out in a straightforward way. And my position is this: these three options are not mutually exclusive.

There is a difference between chance and chaos (in the classical sense). A cartoon world is chaotic (in that anything can happen) and any consistency in it comes from a designer (like Chuck Jones) that imposes order on that chaos or suspends it, as when Coyote finds himself suspended in mid-air until gravity finally kicks in. And not to strain the analogy too much, but if Chuck Jones doesn't design and draw a frame then that part of the cartoon world simply doesn't exist. Chance, on the other hand, operates on a definable set of possible random outcomes. That set of possible random outcomes is constrained by necessity, such as 2d6 producing only whole numbers between 2 and 12. The world of a craps table obeys a higher level of order, i.e. the rules of the game set-up by the players.

So the way I see it, the physical universe displays necessity, chance, and design. Chance because the unique features of this physical universe, its constants etc., could have been otherwise. Necessity because the potentials it is able to manifest seem limited. And designed because the limitations on potential appear prescribed by a higher rational order.