The fine tuning argument for the existence of god (intentionally lowercase) has gained popularity in christian apologetics. The reasons why are actually pretty good. The argument is easy to understand, it relies on real current and generally good science, and there is no absolute refutation from evidence.
In other words it is possible that the universe is fine tuned because a deity did it, since a naturalistic mechanism for fine tuning has not been found. The flavour of refutation sometimes relies on the idea that there may be multiple universes and through sheer blind luck and iteration, our universe came configured correctly for life. I am going to ignore the idea of Earth being perfectly suited for life, because we may not know whether life exists elsewhere and under which circumstances. In any case I see this as a weaker version of the fine tuning argument.
If we consider all the finely tuned variables necessary for a universe that supports life like ours we can make a calculation. We can take those variables, specify ranges and extract probabilities. We can then multiply the probabilities to come up with a rather staggering number that makes it seem almost ridiculous to reject the argument at all. There are essentially two problems I have with this, besides some of the other arguments mentioned in opposition to fine tuning, which I will not mention here.
The first problem is that we do not know which laws act on said variables. We do not know what it is that might constrain their values. The density of any star in our universe is limited to a certain point, at which point the object collapses into a black hole. There is a requirement for the amount of fuel material to jump start a new star also. We may not know what the upper and lower limits of some, or even many of the fine tuned variables may be, because we don't know all the laws that may constrain them in a similar manner to other values we can derive from rules. How then can we calculate probability reliably? Since we cannot know this, choosing a high value of variance could simply be wrong, and it is pointless to even try before we have established underlying constraints. In other words a large section of the probability space might be occupied by sets of values that are nonsensical and impossible within the actual unknown rules that govern them.
The second problem is also of constraint, but constraints in relations. We can say that the amount of oxygen present in the atmosphere changes the size that insects can grow to. If you change the amount of oxygen, the size of insects will also change. Basically each seemingly fine tuned value may not be an island, but could be closely tied to another. There may not be such a large maneuvering space when it comes to different sets of possibilities. If one variable must change as another changes, then their probabilities cannot be multiplied, but must be seen as one. Our incomplete view of the cosmos could be telling us that variables are independent, when in actual fact they form a relation. In fact it could be possible that these relations form complex interactions that move the probability space to something much smaller.
A possible problem with the two points above may be raised as such: If the probability space is much smaller then maybe it still indicates a sort of fine tuning. Maybe if one knob turns and another turns in relation it indicates a willful connection between them. The argument can then be formulated as the probability of the probability space being small enough for the universe to harbour life. As more facts roll in, the argument can become an infinite regress, because each time the proponent of it can say "Ha! Since there is such a small number of possibilities there, what caused those possibilities to be limited in the first place?". The argument then becomes a no-win situation and nothing could defeat it, because its proponents could just keep making up more what ifs and providing the same answer for our gaps in knowledge, namely that god must have done it.
We can put this into perspective, because the fine tuning argument is not new. It is a clever reformulation of the argument from design that was beaten to a bloody pulp by Darwin's theory of common descent. When we stare into a dark room, our eyes can play tricks on us, similarly if we stare into the abyss to try and figure out how something works, our minds can play tricks on us. The magnitude of the universe presents an abyss, and though we can speculate about what lies at the bottom, claiming that god is at work there is answering a question with no real information to answer the question with. I think that when everything is considered we should not try to answer questions even if we have only woefully incomplete sets of information to answer with, lest we behave like kids who are prone to using their imaginations when facts are absent. We are allowed to hypothesize, but believing that a hypothesis is true before testing it is the worst way to try and understand the universe, because in the world of possibilities, there are innumerably more wrong answers than right ones.