1. The fine-tuning of the universe is due to either physical necessity, chance, or design
Support: Seems to exhaust all the possible alternatives.
2. It is not due to physical necessity
Support: On the face of it, there is no reason why the expansion of the universe could not have been a little faster or a little slower, or the amount of entropy couldn't have been a little more or a little less. The best candidate for a Theory of Everything is string or M theory. But it does not predict the existence of our universe. It allows the existence of a large number of universes, but nothing about it uniquely predicts our universe and its constants. Hawking agrees.
3. It is not due to chance
Support: The chances are inconceivable that our universe should be life supporting.
Objection: Any particular universe is equally improbable. If it didn't happen, then we would not be around to see it. Response is to imagine a billion billion billion black balls (the number of non-life-permitting universes) and adding one white ball to it (the life permitting universe). Now pick out one ball, and it's the white ball. The chances against that happening are so high that it's almost impossible.
Objection: We could be living in a Multiverse (as proposed by Vilenkin), with a large number of universes parallel and so the chances are greatly increased. Response is that on the Multiverse model the universe is in a state of complete entropy already, and we are just a random fluctuation of energy within the entropy. But in that case we should be in a much smaller universe, or more likely a single brain (Boltzmann brain) and hence, solipsism is true.
Objection: The anthropic principle says that if observers evolve in a universe, then it is highly probable that they will witness a universe that is fine-tuned just for them. Response is that the anthropic principle says that it is highly probable observers will witness a universe fine-tuned for them, but it doesn't address that it is highly improbable that such a universe should exist at all.
4. Therefore, the fine-tuning of the universe is due to design
Support: From 1, 2, and 3.