I like to compare the fine tuning argument to the odds of my own existence given the vagaries of my ancestry. In order for me to be here in exactly the way I am, every one of my ancestors over the entire course of human history must have met and mated with the exact right person. If my great-great-grandmother on my father's side had married the boy her parents had forbidden her to marry instead of the man they approved of, I might have a different shaped nose, no genetic disposition to diabetes, bigger feet, etc. Or I might not have been born at all. In fact, given the size of the human population throughout time and the size of the mating pool, the odds of every single one of my ancestors mating with the exact person they did is so ridiculously low that it can't have happened by chance.
No, it's crystal clear that some external force must have been guiding each and every ancestor from the dawn of time until my mother met my father, ensuring that they met and mated exactly on schedule (did I mention the two miscarriages my mother had before having me?) In fact, given the fact that many of my ancestors traveled across the globe before meeting each other due to various political upheavals, I think it's fair to say that the majority of human history was manipulated by this external force in order to ensure that I would be born exactly the way I was, small feet, diabetes and all.
Except, of course, that had anything been different in the past then the outcome would have been different and I wouldn't be here discussing it. If you tried to estimate in advance (say, 10,000 years ago) the odds of me coming out exactly the way I did, the odds would be ridiculously, impossibly small. But if you try to estimate the odds now of me turning out the way I did based on my past ancestry, the odds are exactly 1:1.
Another analogy I have heard compares the improbability of the universe turning out just the way it did to the improbability of someone dealing out a shuffled deck of cards and just happening to lay down a complete suit (e.g., all clubs, all hearts, etc.). From a purely mathematical standpoint, the odds of doing this from a shuffled deck of cards are 635,013,559,600 to one. Which is, of course, incredibly improbable and you would be right to suspect that the dealer had somehow rigged the deck in his favor.
Except… let’s say I deal out thirteen cards from a shuffled deck and get a totally random mixture of hearts, clubs, diamonds and spades. What are the odds that I laid down the exact combination of cards that I did? Still 635,013,559,600 to one. How can this happen? Well, it's all because 635 billion to 1 against was the chance of getting it right before the cards were dealt. In fact, now they've been dealt, the probability is actually 1. Talking about how improbable something was that has actually happened already is not helpful.
Similarly, one can look at a lottery where the odds of any one person winning may be 250,000,000 to 1, but the probability of somebody winning the lottery is pretty close to 1 before the drawing and exactly 1 after somebody actually does win it.
In terms of the universe, nobody was around before it began to estimate the probability that things would be as they are today. Had there been someone, then they'd have calculated a very, very slim probability indeed. But here's a universe and here we are in it. The probability of this having occurred is exactly 1.
Again, there are two possibilities. Either the universe was made just to suit life, or else life evolved to fit the way the universe is.
One other point to consider... Let's assume that the "fine tuned universe" argument is actually correct and that the odds of the universe turning out the way it did by chance are mind-bogglingly, infinitesimally small (further assuming that it did, in fact, happen by chance and not because of some immutable laws of nature). How can you say that the odds are any better of it being created by some timeless, immaterial being whose very nature would contradict all we know about existence? How would you even go about calculating those odds? Regardless of how unlikely a naturally caused universe is, you have to first show that a supernatural cause is even possible before you can argue that it is plausible (let alone more probable than a naturally cased universe).